I would agree that fretless tends to have a unique tone that is hard to escape from, but I don't see how that's any different from acoustic piano, upright bass, classical guitar, or any other instrument that isn't EQ'd to sound different.
If you like the sound, use it, there are no stylistic rules in music apart from those that we impose upon ourselves.
PS. IMO, Jeff Berlin may be innovative in his approach to playing, but I wouldn't exactly hold him up as a benchmark of good taste