I don't mean to keep going on and on here, but I guess I will.
As for hot tap water making beer, yes it will. And it will probably make beer that tastes fine, or even delicious. However, if you're concerned about water quality or water chemistry, what comes out of your hot tap is different from what comes out of your cold tap for a few reassons:
1: Lead. You may have old pipes that will leach lead into your water at hot water temperatures. You may also have newer pipes that are lead-free, but have still, under testing, been proven to leach lead at higher temps.
2: Aluminum. We know it's not good for us and has been linking to alzheimers, among other things. Your anode in your water heater most likely contains aluminum, even if it's a magnesium anode. It dissolves and bonds to other minerals, and some of it makes it's way out of your faucet.
3. Iron. Water heaters rust. They also act as a collection point for iron in your water. This stuff gets stirred up a bit, then makes it's way out.
4. Lots of other minerals. As with Iron, things collect here, then sometimes come out in higher concentrations.
Lead and aluminum are no bueno. The other minerals will simply result in you brewing with water that's different from what you tested, or from what you drink on a regular basis.
Them's the facts. Most anyone in the know will say it's not a great idea to drink hot tap water. And lots of folks will say it ain't never hurt them none. I don't see that it's worth saving 10 minutes on a brew day.