First off; what the heck is "intense, long duration sprinting"? And second; are you competing?
That is a relative statement that provides zero information. One would already assume intense since that is what sprinting is; going all out and leaving nothing in the tank. If just interval "sprinting" (not sprinting) that is much slower (though faster than normal speed) if done correctly (unless you are stopping to recover each time which is not doing intervals at all; i.e stop & go sprinting between traffic lights/stop signs). So that leaves us with the vague "long duration". To runners "long" (if in regards to distance) might be anywhere from 25m to a mile given the perspective of the overall length of the training or race. "Duration" indicates a time period so some idea of what that actually is, be it 10 seconds or 10 minutes, would be helpful to know.
Essentially rim depth will make no noticeable difference for sprinting since it is such a small % of the total ride distance so do not be concerned at all about your rims in that regards; especially for non-competitors for which it is primarily for personal taste in aesthetics pr boasting, and has no real application in performance. Your physical condition and technique is what you mostly need to be concerned about. Having a very stiff frame for more efficient energy transfer is way more important than a meaningless rim depth in regards to sprinting on a bike
Also, if you tire width does not properly "match" the rim width you are creating turbulence that has a negative affect. With wider tires you technically need a properly matching wider rim regardless of depth if you want any aero advantage which again only really applies to high level competition where average speeds over a long distance actually provide any measureable gains (average speeds of 25mph or higher over +20 mile or so distances). Remember; all high end parts (components and frames) regardinging aerodynamic efficiency are tested and rated for high level competition not for general cycling. If you cannot perform at that level then the only gain you get is the reduced weight in your wallet. You are merely being sucked in by hype by manufacturers who want your money knowing full well that you will get nothing more than a warm and fuzzy feeling owning competition equipment and the only gain is a potential placebo effect. If manufacturers told you shallow rims were faster the sheep will follow their shepherd's call. All it takes is a couple words and the gullible will follow without actually doing research into the truth of the matter. Manufacturers of competition equipment are not designing and testing their products based on the amateur and weekend warrior cycling community. They are however tailoring their marketing to those who think they need what high level competitors use, and are essentially saying if it works for them it will work for you also, all the while neglecting to state that you need to be at the same level as those who can actually reap the benefits.
Sorry, but I just have to laugh at people worrying about aerodynamics when their riding position will provide way more gain at much lower speeds than having any $20000 TT bike will provide. Other laughable things are clothing and accessories. If you wear any type of loose clothing you have more than just slightly negated all aero gains that may have been had by purchasing any aero designs incorporated into the bike. Accessories also do the same, not even including the added weight. The only real "performance" accessory needed for general riding is a water bottle or 2. And let me ask this: how many of you use a frame conforming bottle over a standard "wide body" bottle? If you use a wide bottle then just scrap all the other high dollar aero stuff because your bottle just negated the gains from the hundreds to thousands of dollars you spent on the competition level gear. (Note: you can flatten and shape most bottles and cages (not CF ones) by heating and reforming).
I'll say again to everyone not competing: STOP WASTING YOUR MONEY AND GET REAL! My best gain comes from riding a lo-pro. Why? Because it automatically puts my body in a more aerodynamic posotion even if riding the top of the bar. I cannot even figure out why riders are so worried about aero gains if they do not have and actually use an aero bar set up (extended aerobar, bullhorn, or drops). Even then I see loads of riders with aero cockpit set ups that never even use them; or if they do the percentage of usage is too minimal to matter much.
You do not need disc brakes if you actually know how to brake. Why can I go over 50mph and safely brake with rim brakes? Modulation be damned; learn how to brake with crappy rim brales and move up to quality rim brakes (lighter in weight, less expensive, and less of a PIA). Unfortunately, the market has sucled in the frame manufacturers into making framescfor disc brakes when riders do not even need then.
Another waste of money for a majority of non-competitive riders are clip-in (toe cage and strap) and clipless pedals. How many of you have those set ups but never or rarely use the ability to pull up during your pedal stroke to thus improve your speed and more consistent application of strength and energy over the entire stroke? They are designed for making your pedal stroke smoother instead of the amateur kiddie style of just pushing down resuting in less speed and efficiency. Folks, you have muscles for that part of the pedal stroke not just the pushing down part. Use them, or forget getting those types of pedals and save on shoes and pedals alike. If you really want to fly up a hill or slice through the wind you need to be pulling up and pushing down at the same time.
If you want get faster just ride more, rider longer distances with harder climbs, wear tighter clothing, and ride in a more aerodynamic position. All of those particulars are free, except clothing (still comparatively less expensive than any component unless going overboard with fashion style or trying match competitive level kits). Even a TT helmet provides more gains than most other bike stuff, but I do not see everyone rushing out to buy them; then again, they are designed to be used while riding in a very aerodynamic position or gains will not be achieved.
Oh, and by the way, just drink adequate amounts of WATER & eat healthy balanced meals properly adjusted for your level of activity, and get proper sleep. Save money by not having to buy foolish "energy" crap that was never needed in the first place. You are all being brainwashed by advertising and marketing. Plus, proper eating will in most cases result in a reduction of girth and weight resulting in a more aerodynamic body and also providing gross weight reduction gains.
So my advice after you have had good meals and proper sleep is it to get out and ride in a more aerodynamic positon (not necessarily TT style), ride low or forward on your handlebar almost 100% if possible, swap to an "aero-bottle", remove all the unnecessary BS from your bike (except safety gear), pedal using an entire stroke (if equipped with applicable pedals), and/or wear tighter fitting clothing and I GUARANTEE that you will be faster although to start you will not feel as good after a ride since your body is not, or cannot do it all at the very start and muscles that you are not normally using full time will need to build up and strengthen. Your body will acclimate (provided no injuries, age, and/or anatomy limiting you), gain strength and gain muscle memory if you keep it up. Who knows, some of you might reach a level where adding the competition stuff will actually help you out instead of it being just a psychological effect and a money burning waste. Just stop reading all the hype and marketing. If only people realized that the amount of time they spend online at home and/or staring at their phone trying to wade through the quagmire of BS instead of utilizing that time to cycle or exercise and get proper sleep they would realize gains they never expected; and guess what, all without any freaking specific rim depth (just to bring it full circle)!
Why is everyone concerned about things not ever meant for them? Yes, a lighter weight bike can make you faster due to the weight diffetential; but that does not make you stronger. If you add weight to your bike or ride a heavier bike in training you will gain strength running the same routine as you would with the lighter weight bike. I would tell you how to do that, but you'd probably prefer to listen to marketing BS about aerodynamics and energy gels.
Just look at what
@GirishH does with basic gear. He does more in one day than what most non-competive cyclists with the best gear do in a lifetime.
PS. Don't call me; I'm out cycling on a 55 year old bike with clip-in pedals, rim brakes; amd without a phone, GPS, energy crap, or a carbon fiber aero bike. Ciao!