An age limit would certainly help things.
A lot of these older officials simply cannot keep up in today's football and it shows.
When I was refereeing soccer , there were two pathways to advancing as a ref. One was High school officiating, and the other was through U.S. Soccer. And in each one, the gatekeepers were the assignors. This system is rife with "OLD BOY SYNDROME". That means that the friends of the assignor tended to get the better matches, no matter their qualifications or fitness level. Of the two, high school was ( is ) far worse, leading to things like a 75 year old man running the line as the assistant referee in a boy's semi final varsity playoff game. U.S. Soccer was not much better until about ten years ago, when the powers that be realized that if the U.S. was going to compete on the world stage, better ways of identifying and nurturing talented referees had to be developed. They began with eliminating "emeritus refs ", guys who at one time had been state or national referees, but who no longer could pass the physical tests or the assessments. They COULD however, get a badge that identified them as EMERITUS NATIONAL referees and they tended to get matches well outside of their abilities. They were the first to go. Then a program was developed for talented young refs to get assigned very competitive matches that us plebes were locked out of with full assessments after each game by National referee instructors, and special training. As well, the physical tests became MUCH more difficult, weeding out yet more aging, high ranked officials. So now there are two parts to U.S. Soccer officiating, us old troglodytes doing youth matches, and a small group of very fit, very well trained, referees doing matches that get them flown around the country, and being taught by MLS, and even FIFA refs. American football has NOTHING that comes close to this level of vetting. I will venture that MAYBE, one or two NFL guys could pass the FIFA fitness test. It consists of six 40 meter sprints, done with one minute between each one, with the maximum time of 6 seconds each. Then there is an interval test of a 12.5 meter walk, and a 75 meter sprint followed by another 12.5 meter walk repeated forty times, that's FORTY TIMES, with the maximum allowed time of 15 seconds per sprint, and 18 seconds for the two 12.5 meter walks. It is the equivalent of 4000 meters or ten laps of an athletic track. You are allowed one repeat of the sprints if you fail them. If you fail to step on the line at the end of the run/ walk interval, you also fail. THIS is the kind of training that modern American football referees should have. God knows that the players are that fit.