Take this with a grain of salt as I own several pumps and brew on both a Brew-Magic and a BrewEasy... which require pumps.
Pumps can be a PITA. They frequently don't prime properly, require some maintenance, and can just not work for some random reason.
That said, your reasoning is why many people get a pump. I have a good friend that uses his kettle to heat all of his strike water up, and then pumps in into the manifold of his cooler tun, underletting. Then uses the same kettle to heat up sparge water, which gets pumped into a second cooler for the lauter. Then he gravity drains the sweet wort into the kettle via gravity, and simply pumps over the HLT into the Mash for a fast batch sparge. Kind of nice as the pump never sees wort - only water.
If you get one, next thing is you will want to recirculate during the mash, etc. Unnecessary complexity unless you like that kind of thing. I do.