The subgenre is called 6DOF, and it does have games. But I agree it's not as big as it could be, and that the magic hasn't really been recaptured. Game developers seem to frequently have this same thought. Descent was good! This should be more popular! Someone tries every couple years or so, but the result generally disappoints.
It is my opinion that 6DOF games are difficult to make good, especially to the standards and expectations of modern gamers. The combat and level design are much more technical (or perhaps just differently technical) than someone from a flat FPS perspective expects, and as a result, the game design seems to have a lot of opportunities for technical mistakes to be made. I think more generic FPS developers, who remembered liking Descent back when our standards were lower, don't realize how much we've learned since then and how very much there is TO learn about the genre.
I find that aggravating. Every few years, the Descent community gets excited about a big 6DOF attempt, and every few years we get disappointed by the result. Even more aggravating, they generally make design mistakes that I think show ignorance of the genre. How does this keep happening? You wouldn't think of making an RTS, or a MOBA, or even a flight combat sim, or really any other very technical genre of game, without the expertise of the veterans and elite players of the genre. And yet 6DOF developers seem to me to do just that. I can only conclude that the problem looks from the outside to he easier than it really is.
I don't mean to sound arrogant! What I mean is that, I think the answer to your question "Why isn't this more of a thing?" is that it's a much harder thing than it appears to be. I think Descent's success can be attributed to a lot of things: to lower standards 30 years ago, to lucky or prescient design decisions, to a brilliant team enjoying the unique freedom of the wild world of 90s software passion projects, and to a lot of community involvement over time. And I'm not sure that's the whole list. I do think it should be a bigger thing now - there is a delicious flavor here and no reason this generation shouldn't love it too. But it's also apparent that Descent caught lightning in a bottle, and even I couldn't tell you everything that went into making it happen once but not twice. I can point to reasons that I think attempts to repeat it have been less successful, reasons that make sense to me as an expert player in the genre, problems I think I or a couple dozen pilots like me could help anyone avoid. But I'm not sure that explains all of the difficulty. Every now and again, some veteran pilot will take the problem into their own hands and try to make the next big 6DOF, and those projects are rarely finished and rarely good. It doesn't seem that hard, from a software point of view, and they know the game! Or think they do. And yet they fail. So genre expertise can't be the only ingredient, even if I think it's a necessary and usually missing one.
The problem is clearly harder than it looks. I think I know what to do, or at least one piece of the puzzle, but better warriors have been slain on that battlefield, and I haven't actually made the attempt, so I don't actually know. But I can definitely say this much: Developer beware! Here there be dragons!
Overload's good though. :)