So recently I found out about this and tried it for myself. Such a cool feature! Although I prefer my 30fps eyecandy, I must admit to the 60+fps crowd: GT1 plays infinitely better in 60fps (50 in my case=PAL region). I also made a nice comparison between the normal GT1 mode and the 60fps mode on all 3 tracks, on which the high-fi mode is available, with commentary (written) and all that jazz, so check it out if you like!:
I've been itching a ton to play the first Gran Turismo at 60 FPS... or 50 FPS. Sadly, it seems like Emulation is taboo around here, so I can't really talk much about it.
Just get a used PS2/GT1 If you have a modern HDTV with only HDMI ports, then you'll need an adaptor though.
Contrary to the common belief, every PS3 plays PS1 games. Probably easier nowadays to get hold of one of them than a PS2.
The only time I've ever had issues with it turning off Analog is when the controller is charging. Other than that, I never have had an issue with the controller.