I think the hard part to get around is the "one rep max" thing, it sounds much more intensive than it really is. Its not a competition maximum, and to be done at a good speed as should all of the compound lifts, but thinking in terms of "progressively heavier singles" would really be more accurate.
I have done all kinds of different things in training and programs like smolov that have no degree of autoregulation at all are much more draining and fatiguing than working up to a daily max and backing off for a few rep sets. There are construction workers, loggers, etc. whose daily requirements would make this program seem like a cake walk, its just a matter of time and adaptation.
imo its just a matter of trimming off all the fat and getting to the meat of what you really want to accomplish. When you cut out tons of assistance exercises, tons of sub maximal work, and other things that dont contribute as directly to your goal, you have a lot more room for recovery from something like this. I have run 5x5 templates that were harder to recover from than training this way, and not nearly as effective at increasing 1rm. much more stress to the tissue with the 5x5 and much better hypertrophy gains.
One more thing, when training this way, its not like you come in each day and pr, that may happen very early on but what Ive seen is you hit a pr of say 450, then the next day you work up to ~450 again, the next day, 450 again etc. Finally in a week or so, you hit 460. You have been squatting at very near this poundage almost like a habitual event, its not a "dangerous" or rare event, that you have to get nervous or amped up about. I really think that is somewhat safer to train this way if training in a lower rep range and 1rm are important to you, people who get hurt maxing out are people who dont do it much and arent prepared for it. This was always one of Louie Simmons big pet peeves with other pl training methods, even though they would rotate the exercise, he strongly believed that you needed to do heavy singles to be able to lift heavy singles safely.
Best thing to do is,( a. if you have been training long enough to even consider this and cant still make linear day to day progress on a 3x a week full body schedule), try it for a while, just start out eeeeeeeaasy. I have some of my athletes go up to a single, then do back offs with trips, but they train 3-4 a week, so I add a rep set at the end. IMO that is even more effective for a majority of team sport athletes, as hypertrophy is important for them as well.