Incredible insight, but I fear it won't work out well: when the option is there and ubiquitous, websites will rely on it, so disabling features is basically choosing to save some of my resources in exchange for a broken web experience.
Since I'm doing 3D graphics in Web Browsers, I consider not having 3D graphics APIs in Web Browsers a broken web experience. The browser is the easiest and safest way to distribute applications with virtually no entry barrier to users. I don't trust downloading just any binary and therefore I won't execute them unless they are from a trusted source. But with 3D in browsers, I can trust any web site not do damage my system and try a large amount of experiences that others create and upload.
There are applications where the point is 3d graphics. I don't object to letting them use my gpu if they ask nicely. There are other applications -- really the vast majority of them -- where 3d graphics is completely beside the point, and has nothing to do with the reason I'm on your website. That is my concern: that that second class, being the vast majority, will say, "hey, I have access to all this compute power, why don't I just throw some of it at this needless animation that I think looks cool, or at this neural network, or at this cryptominer". Past experience suggests that this is a reasonable concern.