As an aside, stop bath stops development because it's acidic. Rapid fixer is also quite acidic and will also stop development very rapidly, so why bother with a stop bath?
IMHO the reason is to preserve your fixer from carryover of alkaline crap from the developer. The stop bath is not just stopping the development, it's a matter of dropping the pH of all the stuff soaked into the emulsion so as to not stress the buffering agents in the fixer. This is not so important with film (a water stop bath is fine there, it just washes the developer off) but is very important with FB paper.
If you develop some FB paper, it will soak up a huge quantity of developer like a sponge and then if you dump it in your fixer, it is like chucking 50mL of developer into the fix. The fix will survive that once or twice but not in the long term, and you will not get the rated capacity of the fixer if you pollute it with so much developer. The stop bath exists to wash the developer out and bring its pH down to closer to what the fix needs, so when you carry over a bunch of stop bath into the fixer, it doesn't really do much damage.