GTA: San Andreas on the XBOX did allow you to use such a feature, provided that you had used the XBOX's disc drive to rip the audio CDs yourself. I recall letting the XBOX rip all of my System of a Down CDs circa 2005 for expressly this purpose.
PC ports, IDK. Probably.
They later extended it on the Xbox 360 to allow you to link in your Windows Vista machine to stream your MP3's straight to it
Playing Halo 3's campaign to Queen was a great experience back in 2007
The Xbox 360 expanded on the feature in some neat ways -- if you had an iPod or other portable player, you could plug that in via USB, it supported generic DLNA shares (so you could play music from Kodi/XBMC running on a PC), and some (most?) games would flag cutscene audio vs. in-game audio, which would allow the system to pause the user-provided audio and fall back to the game's soundtrack for cutscenes.
It also had global settings for controller vibration, inverted camera.. perhaps some others? I really miss those in future generations and on PC.
Yes. Source:
After loading, the entire game (from opening screen to ending scene) fit completely into the PSX's tiny RAM.
And the in-game background music was just regular CD audio tracks on the game disk, which was easy since the drive wasn't used for anything else anyway.
Open the drive, swap disks for your choice of audio CD, and it was happy to play those tracks instead.
(Or, alternatively: Put the Ridge Racer game disk into a regular CD player and enjoy the synthwave soundtrack all on its own.)