There are tons of games that take inspiration from NES, Gameboy and SNES titles - but what about taking inspiration from N64 and Faux-PS1 games?  
 
The 3DS remakes of N64 games - they seem on the brink of  "faux-N64"? I dunno - I grew up with the N64 and PS1 - and that's a nostalgia market largely untapped.

There are already cutscenes in Amped 3 that make fun of the way FFVII looked. As far as actual homages I don't think  they will ever get remotely close to the level of new pixel games (cause pixel art can look nicer without giving away it modernocity) but I guarantee that there will be real games released that emulate the style of PS1/N64 games as soon as kids who got that as their first video game system start to become primary breadwinners for their households.

I sure hope so!

I think you may need to wait til next generation.
Its a confusing one because, at the moment at least, if you release a game with PS1-era-graphics people will still be unsure whether you're joking or not. Its too soon almost. With stuff like 8-bit, we've now got to a stage where it was so long ago, and we can actually make the 8-bit look modern in an ironic sense (see 3D Dot Game Heroes). So maybe next gen, when it'll have been going on 20 years since we had PS1 level stuff, and people actually regard it as retro.

I hope not.  A game being done in the same style of Mario 64 or something like that could be fun..  But NES/SNES games had a certain charm to them.  Many PS1 games, especially early ones just looked bad, I don't know why anyone would want to see that style emulated.

It would be funny, but certainly not very visually appealing.

Maybe for humor, but the difference between that gen and the older gens are that people play 3d games now, and to emulate them would just make them look like shit. NES/Gameboy etc. titles are mostly sidescrollers/other shit, which still basically play the same so it's less horrible to imitate.

Perhaps. But as WinterSnowBlind said, low poly 3D models with muddy textures dont even remotely hold up as sprite art. Personally I would love to see another build or doom engine FPS.