It is definitley important to leave grass clippings, not spray toxic chemicals, allow diversity in different grasses and broadleaf plants etc. But I'm not sure that not watering is a good idea unless you're in an area where water is scarce like Arizona. I live in the PNW and we do not have water issues, and if we did it's a reservoir size issue not a rainfall issue which is easier to fix. Like currently my reservoirs are both sitting around 80%, at the end of summer, in a year where we received much less rainfall than normal, and will be 100% by December. A brown hibernating lawn is not sucking in CO2, I dont think its providing food, flowers or habitat for foraging insects, it's just not really doing much. My approach is to allow and plant a variety of different ground covers, mow very rarely, and water it a couple times a week during the summer. Water conservation is not the issue in my area, habitat loss for bugs and climate change are the issues and not watering seems to do more harm than good. (I know most lawn grass arent particularly efficient at it but it's better than nothing).
My mind can be changed though.
I'm hopeful we're going to start seeing an end to lawn culture though. I think that's a boomer thing who got brainwashed by monsanto marketing in the 60s-90s. If people let their lawns become more meadow it would probably go a long way. I do think there's a potential market for a non-profit that converts peoples front lawns to natural meadows or farms it.
Also the lawnmower parade sounds hilarious! While odd I bet the people doing that have a lot of fun.