We use flight following on most flights in our area. The only time
it's ever a problem is around (the very busy airspace of) Chicago,
where (ironically) we could most use FF.
Usually Chicago won't accept a hand-off from adjacent controllers, and
if we try to request FF they will reply "unable." Not that it really
They can't drop you if you're IFR. :-) (hint hint)
of course, there's no guarantee that you'll get a clearance either...