I probably own more three-point bridges on basses than most people here do.
I had a handful of cases where I had to file the slots deeper (never on new saddles, too high saddles were mostly an issue of the seventies), I'd say one out of 10 at the most, my singlecut prototype Ripper from the early seventies and my LP Signature come to mind. Both are basses where the neck is set too low and the bridges feature ultra-high seventies saddles hence the issue with the filing (which you wouldn't be able to do on most other bridges, so you'd be stuck).
Your issues are beyond me. I'm a no-buzz, perfect intonation, low action (but totally buzz free) OBSESSIVE, yet setting up a three point never fills me with dread, I have yet to encounter one I could not get to work, that did not have sufficient intonation range, did not accomodate my desired action etc ... The only three point I ever replaced was the one on the Blackbird and I did that just to give the Hipshot replacement a try (which is in no respect significantly better, who needs a TBird with a little more sustain when the bass is already very "sustainy" as is), the original bridge was fine. I've never had an issue with saddle pressure (even in the few cases where I had to file).
What I do like about the three-point ist that all you need is a regular size screwdriver for intonation and a man-size one
for the studs and you're all set. Everything is freely accessible and you have all the torque in the world adjusting, no fidgety easily lost hex keys in weird sizes that get gorged.
The three-point, comrades, is the Stormovik, T-34 or Kalaschnikow of bridges!!! Fool-proof even in winter offensives.