Grass eventually responds to a more nitrogen rich soil by out competing the clover (which actually prefers low nitrogen soils), assuming you are not butching it to one or two inches, which our northern turf grasses hate. Even some of the shorter grasses like Bermuda or St. Augustine can get happier a little longer; more shade on roots means cooler soil temps, means less competition from C4 tropical weeds like crabgrass, and better water retention, therefore better soil biologies, so more nitrogen and phosphorus, and better soil tilth...
Or you can go chemical and screw that all up, and cut at two inches and fight the summer weeds (or use more chemicals), increasing your thatch layer, which encourages chinch and sod web worm (I saw a few in my lawn this season already, but the robin's are in my lawn in force and I trust their god-given abilities) so you'd have NEW chemicals to put down...

So AS, toss that pulled clover in the pile for best effect. And Haesuse, me too in the worst way. Negotiations are back on, but not going well. I miss my angelfish...and the tank water. That was my houseplant regimen...
HG