My impression from reading articles and technical reports about this is that there's a couple of things going on.
First, I think the wider-tires-are-faster argument has to be appreciated in the context of the narrow-tires-are-faster argument that dominated for a long time. With the latter paradigm, you wanted your tires as narrow as possible, with some lower boundary constraint due to wheel and tire thinness limitations, maybe around 20-21mm. The former paradigm emerged in part in contrast to that, in that "wider" doesn't mean "infinitely wide" but rather "wider than what's typical for people striving for narrower tires". Some of the arguments about rolling surface area are maybe understood in that context -- the patch of tire in contact with the road maintains the same area as a minimal area under the narrow tire paradigm, and then it starts to become larger, at which point you start increasing friction theoretically with more tire surface area in contact.
The other argument for wider tires is about impedance gains due to wider tires -- decreased vibrations basically. This is different than decreased or equal rolling resistance per se. However, there are eventual aero losses for wider tires, as well as weight increases (which then increase rolling resistance). Eventually these aero losses and weight increases overshadow any impedence gains, and the wider tires' costs exceed their benefits.
This is the sort of thing about cycling that is frustrating to me. I love cycling, but so many mechanical factors get really oversimplified: costs aren't often realistically assessed against actual gains, and sometimes gains are very restricted in the circumstances under which they apply. Disc brakes, for example, are safer, but you see little discussion about whether the safety margin they afford actually would make any practical difference in scenarios in which accidents typically occur (e.g., where a car is coming from the side or a blindspot), and they're often heavier and less aero (so yes, they save your carbon wheels, but you almost have to have deep section carbon wheels to make up for their weight and aero costs to begin with). I'm not saying disc brakes are a bad thing, but I think in practice their gains are more complex than is often made out to be. In the same way, wider tires are probably more optimal than a lot of people thought in, say, 1985. But I think the pendulum has swung a bit too indiscriminately in the other direction at the moment. What's probably most accurate is to say you want the widest tire that affords some impedence gains given your typical riding surface, and not anything wider.
Aero effects increase exponentially (?? polynomially?) with speed (that is, as your speed increases, aero effects become more of a factor in further speed increases), which would match your experience. As your speed increases, the wider tires become more and more of a burden, and require higher wattage to compensate for.
All sports with any significant tool involved are full of misperceptions and myths, not supported by science. Cycling is full of them, but it's not the only athletic discipline like that.