I don't know where OP got his "drastic difference in gameplay speed and music" in "almost every console from the NES to the Dreamcast". I remember such a thing from one game (there were possibly others but they were rare). The game was the first Sonic the Hedgehog for Mega Drive, where the lazy PAL port features slowed down music. Sonic 2 and all later games in the series were fine though.
Anyone with enough knowledge care to clear this up?
Depends on the games. It's quite possible to produce a perfectly acceptable speed-corrected 50Hz PAL port.
In simple terms, assuming a perfect framerate:
PAL at 50FPS = Each frame represents 20ms of time
NTSC at 60FPS = Each frame represents 16.6ms of time
The problems come about when they don't *account* for that change in the conversion, so the PAL version takes 20ms for 16.6ms of time to elapse.
It's quite possible to instead adjust the code on the assumption that 20ms elapses each frame rather then 16.6ms. That said, though, it's worth adding a mention that that's much easier in polygon-based games (where interpolating to find what it looks like in the interim is trivial) rather than in sprite-based games (where you have to choose one sprite frame or another to display, you can't get the interim one)
Ikaruga on the Gamecube is a good example of a game with heavy sprite usage with a 'good' 50Hz conversion but still notable flaws; that simply skips every sixth frame of each sprite. If you're looking for it it *is* noticeable, so it's not completely perfect, but it is acceptable and plays at a decent rate as a result.
In this day and age, though, offering both choices strikes me as completely acceptable. Nintendo aren't averse to offering NTSC 60Hz content for download as long as they pile in plenty of warnings, but they do seem a little reluctant to do that for PAL-released VC titles. I wonder if they're simply averse to (effectively) giving you two copies of the game?