A lineman’s belt is used in an effort to stabilize you and allow to be hands free and work, not prevent a fall. As stated, falling with a lineman’s belt usually ends up with a better result for the climber than no belt.
A tether is designed to prevent a fall.
Rock climbing harnesses are designed to be tied into dynamic rope in a system that allows for give in the chain so it absorbs energy from a fall.
The tethers 99.99% of us use are not dynamic, they are static. They do not stretch - meaning you will feel the entire force of your fall. It doesn’t take more than a couple feet to generate a force strong enough to make you regret falling.
My advice would be that a tether used as fall restraint is not a bad idea - given you understand how important it is to keep it above you, and minimize slack in the system at all times- even if it means taking an extra 35 seconds each time you climb.
However, one tool doesn’t replace another. If you don’t want stability while climbing(you really need to consider that the name of the game is minimizing opportunities for falling - ie stability), and just want to prevent you from falling, tether will do that job. If you want stability and fall prevention, tether and lineman’s are both needed. There is a tool that combines function, called a tree squeeze. It may fit your style.
I personally use a lineman’s, and do not hook up tether during a climb, save for two circumstances: a step or move that requires me to extend beyond my comfort zone in the lineman’s, setting up at height on my platform.
Having said that - I use a lineman’s belt properly, and climb very slowly and carefully. I cannot imagine how people climb without them as it makes things incredibly efficient. But I understand we all come atthis from different perspectives.
Understanding what each tool is for, and the risks in using them, is imperative to making the right choice for you. Assuming they do things they cannot is what puts you at the base of the tree faster than you intended!