Most of my basses over the years were neck through axes, primarily 80's BB Yamahas and Alembics.
I far prefer them to a set or screw-on neck, for these reasons:
They're all typically laminated necks. This tends to be stronger than a typical two-piece or occasionaly one piece neck. I've never seen a twist in the ones I owned (and Alembic, like Rickenbacker, uses two truss rods to where supposedly you could 'offset' the tension in the two to remove a twist), and typically once over their new days where the wood may still think it's a tree, they rarely required must adjustment in the ones I owned. All of mine also had ebony fingerboards (a VERY stiff/strong wood) which tended to act as extra reinforcement besides the neck plies themselves. And in my experience, the stiffer and harder a neck is, the better 'isolation' or definition of the notes played, and this can be very helpful of 5's or 6's in terms of making nice, tight low C's, D's, etc.
They typically tend to be 24-fret instruments, so you have deep cutaways (and a smooth neck to body intersection since there's no joint where the two were mated together) making reaching up to the octave and above far easier if you want to play 'up there'. The down side to this is it cuts into the available 'real estate' on the body, so often on these types of basses with two pickups, they can seem closer together than other designs, but you just don't have as much room to space them out further. I really miss not having that smooth heel at the back of the neck, I HATE that neck block on Fender-style instruments.
And something I saw in varying degrees in mine, if you have good ears, that you tend to hear the fundamentals a bit better in a neck through. This can be very dependent on the particular wood in a given bass, and it's a subtle addition to the tone, but it can be there. Separate neck/body instruments tend to interrupt that but can induce that 100-200hz push that is so noticeable in good Fenders or Fender clones. But the low grind of the 1st and 2nd harmonics I heard with one of the Alembics very noticeably was unique playing in the lowest notes.
It's a crapshoot indeed if you had serious problems with a neck through, I just never saw any, and would think that only in case of the most dire problems, none would be beyond the capabilities of a 1st class repairman. I've heard of the occasional 'heat bend' from time to time, but that's pretty rare.
I prefer them, and if anything to me, they take less maintenance than more traditional designs. Like any instrument, their long term performance is dictated by how well they were designed and built, and if buying used, maintained by the previous owner(s).
