Loaders doent lift vertically, they go in an arc just like your 3pt. It isnt quite as dramatic as the 3pt across the 4' PHD range, but its close.
When I was putting in my fence with a crosbar I put it in 1 post at a time so we could precisely align, & plumb each one. I had a couple helpers & one of em would stand to the side & let me know when to bump the go pedal a hair to keep the auger level on it's way down. That was with my 3pt, but similar issues with the new SSQA mount PHD.
Posts stay tight if you tamp the backfill in really tight. If you dont tamp it hard they loosen up. I upgraded from a 9" auger to 12" for my 6" posts. It let me hsve wiggle room to get the precise alignment I needed. No matter how good you work things, post holes aren't perfectly aligned or plumb. That means you need room to shuffle the post in the hole before tamping things in tight.