Slowdown is ultimately caused by a game having too much work to do in a single frame than it has time for. Hacking a game to use FastRom is one [simple] option that works for SNES. But another option would be to just go in and optimize the code so it doesn't use as much CPU time.
There are a number of games, particularly on the NES, which infamously do a TON of work during a single frame. Battletoads is well known for its optimization efforts, and I know nothing about the game code, but Recca on the NES does an INSANE about of splitscreening and spritework every frame with no noticable slowdown.
So while FastROM is a nice crutch to speed up a poorly optimized game, it isn't strictly necessary. You could just make the game not so poorly optimized. Of course, that is more difficult because it involves analyzing the code, figuring out what it's doing, and finding a smarter way to do it.
But often, small improvements make a big difference. Code slowdowns often pile up in looped code. So shaving 5 cycles off some code that is called 40 times per frame makes the game effectively 1.5 scanlines faster, which MIGHT be enough to make it not miss the next frame and eliminate all in-game slowdown.