From all the info available and interviews I read back in the days when Cobain was alive, I just don't think it would have lasted as is, he didn't seem to be real happy with it IMO.
As for the bridge/tremolo, if Kurt had have been around it would have been changed to either the jazzmaster tremolo and tune-O-matic or a gibson style stop tail. I remember Kurt saying "I hate the jaguar tremolo...but I hate all tremolo's, so I block them off".* (He actually had a block of rubber inside his jaguar tremolo to stop it moving)
I also remember him saying "the mustang tremolo gave/gives me a lot of trouble"*
*or something to that effect, not necessarily word for word!.
IMO, the jazzmaster tremolo (I say jazzmaster trem because the jaguar doesn't have its own trem, it uses the Jazzmaster one which was designed in 1957 or earlier) is the most aesthetic whether you use it or not, I think Kurt liked that about it and the fact that it had a third bridge.
Also,IMO, the mustang vibrato is actually pretty decent, it works perfectly when you set it up right or it can work as a stop tail if you adjust it so the bar tilts back, this way it only goes down pitch and cant be knocked out of tune.
Whether or not Cobain would have modified or kept the Jagstang comes down to personal opinion. I try to base mine on facts but its still subjective as he can't speak for himself.
if you like the Jagstang, play it, if you don't but like the idea of it, build one closer to his drawings like I plan on doing!
I'll buy one of each color jagstangs (first issue) some day, purely for collector purposes and I'll hang them on my wall and post a plaque under it saying "the guitar Kurt Cobain tried to design but fender phucked him on it!" 😁