To have a good serve, fundamentally you have to put the ball in front of the racket. This has nothing to do with ff'ing, it has to do with where you start and if you end on the line, you can dance like Fred Astaire if you want--but just don't touch or step over the baseline or the center hash.
You're assuming they lose balance. They have good balance, it's just a few inches forward of where it should be. It's consistent.
It's not a logical impossibility, but it's harder to stay in balance and have a solid, repeatable motion when you move a lot. First and foremost, it's hard to get the toss right.
But, this a relative concept. My idea of what a "good server" is might be different than yours (see BlueFan75 post #98).
I can say that my serve would improve from a consistency standpoint if I could stop taking that step. On days when I'm "not feeling it", I can serve a lot of faults, and this stepping and moving is the root cause. It complicates things. It's very inefficient.
But, once something is ingrained, it's really, really hard to change. Understanding this and understanding that rec tennis players aren't professionals, I overlook ff's and many other minor rules violations at this level of play. Others don't see it that way.