Those MIM P basses are certainly not created equally. I've owned two, and played a half dozen more. In short, the good ones are basically one unit of P bass. They aren't the bass Jamerson played, they aren't a signature model and they aren't trying to be the sort of P bass that rattled off the production line in 1957. They are the basic ticks-all-boxes P bass and, as a blank canvas, they serve as good basses. They don't get my pulse racing by any means, but they are usable 'cooking' basses and can be modded easily as they are real Fender and made using real Fender dimensions.
I've encountered the issue of the slot in the tuners being too tight, especially for a silk-coated E string. Those MIM tuners are an odd size, and only Hipshot (I think???) make a drop-in replacement.
The ceramic capacitor might be 'cheap', but as long as it works it works. No need to sink an Orange Drop cap in a bass like that as it makes no difference. From memory the pots are CTS-brand with indentations in the back and a small hole that the base of the shaft protrudes through. Perfectly usable pots, though maybe the taper wasn't the best choice if the tone control is too binary in its function.
The trapped wire is annoying, but it happens. I've done it all the time, especially with P basses and Strats where you're screwing down a vast, flexible plastic sheet to the front of the instrument. It does indicate that the bass wasn't rigorously scrutinized before it went out the door, which I find slightly worrying.
The sharp fretboard sides are simply because it would cost more, either in time or expense, to either pay a worker to roll the fretboard edges or to somehow machine a roundover onto the fretboard edge. In turn it would make fretting the board more tricky. I tend to roll the edges of new necks, but I also like to check the frets are properly leveled and crowned, so I'm maybe more of a tinkerer than the average bassist.
A broken Allen Key takes proper skill, so I hate to think how that happened.
High action is quick to fix. The back bow in the neck is alarming, especially if it can't be dialed out.