HTupolev

If you add an entire kilogram to your rims, that's less than 50 extra joules every time you accelerate from 20mph to 25mph. Up to a few percent more power will be needed if you accelerate over the same duration, or things will stretch out a tiny bit farther than normal. It's something, but only during a very small fraction of riding time on most roads, unless the paceline is being extremely uncooperative.

Bikes that I take on road rides vary over a 13-pound range, sometimes several pounds of that from the wheels. It doesn't really seem to have tangible impact on which pacelines I can hang with until gravity gets involved.

The increase in profile from a wide tire is pretty tiny compared with something like the profile of a rider. It's also in line with the bike, so under most circumstances there's lots of self-drafting going on to ameliorate the issue.

Where the aero penalties can get a bit bigger is in the indirect sense of available equipment. For instance, if you want to build up a fancy aero bike with high-performance road racing aero wheels, choices are marginal for nominal tire widths higher than ~28mm.
But the actual builds on lots of ordinary road bikes are in this same boat, and this doesn't seem to dissuade people from considering them to be capable machines for spirited riding. If someone shows up to a crit on a stock Tarmac Elite, few people would tell them to go get a real road bike.