When you look at HED’s own aero data, the H3 series is fast, but not faster at zero yaw than deep spoked wheels, and it stays very consistent across a range of yaw angles, whereas deep rims get faster up to the point that they stall. Unfortunately, HED pulled the aero charts they used to show off their website. Below is an old graphic from Zipp.

Based on this, the H3 can’t compete. But, Team Sky, with the biggest budget in pro cycling and a philosophy of marginal gains, used them, and now uses the Shimano 3 spoke. Tom Dumoulin, a favorite to be the next TT world champion, just scorched the Vuelta TT on a 3 spoke front.
Clearly, something else is going on here. I have heard that the way the 3 spoke interacts with the fork improves its performance beyond what you see in the wind tunnel, though Sky’s Pinarellos have forks with very wide legs to avoid turbulence from the wheel. Clearly, teams with a lot of resources and interest believe it is the fastest option for their riders, though some TT legends (eg. Tony Martin, Fabian Cancellara) use “conventional” wheels.
And, as already pointed out, what pro cyclists or triathletes use may not be relevant to mortals. Top TT riders average over 30mph, so they don’t see much yaw. I average…well…somewhat less. As has also been pointed out, your deep wheels may not be helping you unless they are also scaring you, since their advantage is at wider yaw angles.
The H3 went out of favor for a while because it requires a very narrow tire to perform well–19-20mm. Pros have gone to much wider tires for better comfort and lower rolling resistance. HED developed the GT3, which is tubular only, at the request of pro teams a few years ago. Same design, just wider, so it performs well with a 22-23mm tire. At Eurobike last week they showed a new H3+ that uses their 25mm wide rim.
Personally, I retired my H3. I loved the way it sounded and behaved in crosswinds, but a 20mm tire at 120psi is not as nice to ride as a 25mm tire at 100psi…it looked and felt like you were riding an ice skate on the front. Chances are the aero gains of the narrow tire were offset by the better rolling resistance of the wider tire. But the H3+ has me interested, especially if they release it in the blacked out rim.
Because, let’s face it, we are age groupers. Our potential performance is enhanced far more by feeling fast because you look fast than it is by a watt or two of drag savings.
So, it comes down to who you want to be like–Wiggo, Froomey and Dumoulin, or Der Panzerwagen and Spartacus.