No, FBlit on an A3000/A1200/A4000 is faster than the blitter for some chipmem to chipmem copies. The blitter can't saturate the chipram bandwidth, while a really fast CPU can. I don't know what CPU it maxes out at. It also has the added benefit that icons etc can be stored in fast ram, which makes it even quicker. However things like full window dragging are sped up with FBlit and that doesn't touch fastram.
Of course, but the best speedups come when some of the data can be handled in fastram. As you said, chipmem maxes out at some point, but you can still benefit from the tasks that can be done elsewhere.