We started using Paychex when we had a total of two founders, making almost nothing, five years ago.
It was painless -- and cheap. On top of that, Paychex has had our back with hands-on personal customer service when things went wrong due to the usual paperwork screwups by NY State.
I'm truthfully not sure what Paychex could do better. This isn't an area where -- as a tech company -- we want things to be particularly technologically complex. A real person makes all the difference to us, and its not like Paychex is a significant cost for what they do, reliably.
Truthfully, I don't know why you'd badmouth them as "legacy solutions" that "don't really work". They've worked great for us, especially as we've expanded to offices in multiple cities and states, with all the attendant per-locale paperwork overhead.