Happy to give my thoughts on this; as I said, others certainly have other opinions to share.
I think it’s far to say that Flys are not for everyone; they have a unique look, feel, and sound, and, to paraphrase Ned Steinberger: “look, feel, and sound”, in that order, are what most people use to inform their guitar purchases. I do feel that Ken Parker was/is right when he said that he built the Fly for the “80th percentile”; it’s not for everyone!
If you’re looking to get a Les Paul sound, you can buy a Les Paul and it will just work. A Fly is versatile: it has great-sounding pickups that represent clearly what the instrument is doing and “what the instrument is doing” is sounding like the most timberally-balanced instrument you’ve ever played!
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You can use the Fly as a starting point to sculpt a Les Paul sound, but it doesn’t sound like that out of the box; I think that’s where the problem begins for most people regarding the Fly’s inherent timbre and the pickups.
I don’t think we can say that all guitarists have the same understanding of how to dial in a good sound on their guitar or on an amp. A telecaster into a Vox, for example, is a combination that just seems to work without much extra knob-tweaking, but, with a Fly, you have lots of options, which makes the Fly quite versatile, but I don’t think most guitarists know what to do with those options.
For example, the fact that you can blend in the piezo with the mag pickups or route it out separately; I hear people say “nobody uses the piezo”, but that’s not really true. If you are open to learning/experimenting with what that acoustic-ish timbre blended with the mags can bring to your sound, then the Fly is a great instrument and very versatile! I think the versatility probably appeals to a certain type of player, but, again, it’s not like plugging a Tele into a Vox.
I should also mention: the Fly is very easy to play and very transparent: what you play is what’s going to come out with a nice strong signal and a very pleasing timbre. If you are a sloppy player, I think the Fly is less forgiving than other guitars, which have “a sound” that masks a lot of the nuance of what’s being played.
So, the pickups take the blame for the Fly’s overall timbre, but really that’s not entirely fair: it’s probably that the whole guitar is a mismatch for some players.
The Fly has incredible sustain; you don’t need to rely on the pickups for this whereas other guitars do! The Fly has an incredibly even and consistent tone everywhere on the neck; other guitars need to rely on the voicing of the pickups to compensate for areas of the guitar register that sound thin or too muddy.