IMO, and not denaying the zoom utility, the primes have a really strong advantage, but much more chalenging. They oblige to move physically on the scenery.
Moving physically has the consequence to be part of the scenery, and therefore being involved deeper.
Even if you are strict with yourself and let's say you use the zooms as a fixed focal lens, soon or later there is this temptation to play instead of dispacing physically.
Since I started to do street photography, about six months ago, I now only take one prime in my bag. Or a 50mm or a 28 o 24mm. Sometimes a 16mm, rarelly.
It is way more difficult but that is where I learn most, and much more rewarding when it works.
Just a thought: if you can do street with one prime and get great results, you can do anything else. I really realise this more and more.
Cheers.