Loctite, depending upon the version, fulfills multiple roles. The lighter-grade stuff isn't so much of a bonding-agent as it is a gap-filler.

What's happening with the OP's bike is that the already-large clearances between the BB and shell may be a little more than normal do to manufacturing tolerances and/or too many thread-chasing operations. Facing a BB ensures proper 90-degree squareness between the lockring-face and the spindle-axis. This does help lock the BB in place... laterally.

However, it does nothing about vertical movement. When you tighten the BB into the shell, the threads are pulled laterally into each other and the tension/stretch of the threads provides friction between the threads that keeps it in place. But the vertical gap, the difference between the ID/OD of the thread is still present. Then with vertical forces from pedaling, the BB will move up and down, grinding the threads against each other and cause squeaking.

This is where a gap-filling compound comes in handy. Grease sometimes works for small tolerances. But if you've got larger gaps, then a hardening compound that solidifies to fill the gap works better, such as Loctite 272 or the grey stuff that Shimano uses. It's the gap-filling function of Loctite that we're interested in, not its adhesive properties.

That's also why teflon-tape works as well, you just need to add as many layers as needed to completely fill the gaps between the threads. I've had BBs where 4-layers of teflon-tape still causes squeaking, while 6-layers is too thick to thread on. Then 5-layers is the perfect amount to fill the gaps.