The corner brackets actually have reinforcement brackets backing up the sheet metal where they attach, so all of that was added for a reason.
I converted my ‘74 over to the ‘70-73 style bumper and brackets. The sheet metal reinforcements for the outer brackets are kind of a pain in the *** to add to a complete car that didn’t have them, so, I just run the main brackets. Car has been that way for years, no issues with the bumper, body gaps etc.
So, will running without the brackets cause you any issues with the bumper? Not as far as I can tell, at least as long as you’re not in an accident.
But, I’m equally sure they’re there for a reason. It’s not cosmetic, because they don’t affect the gaps and the bumper stays in place on the main brackets without them. Bang the corner of the bumper on something without them though and I would bet the bumper would bend at the main bracket and hit the quarter.