Chamberlain, Ruth, Aaron, Bonds, Dimaggio set their records in competition. Someone may well have hit more home runs than Aaron in batting practice, but that's practice, as was John's record. The high run record belongs to Darren Appleton, who ran 200 and out in competition.
Suggesting that people are particularly interested in records achieved in practice in sports is nonsense. Ted St Martin made over 2700 consecutive foul shots in basketball, and yet his name is virtually unknown. If memory serves, the record for consecutive spot shots made is over 2,000. Guess who did it --- I have no idea, because as it occurred in practice, it doesn't matter.
People like numbers in sporting competition. In practice, they're not very interested, and frankly, why would they be?
I think the Ted St Martin number is actually somewhere around 5000, which further proves your point.
As to the other post, and to further agree with you, I only know of Efren winning the Derby 1pocket division 4 times. Other than that, I don't think anyone has 4-peated a major open tournament ever in the modern pool era, and its hard to imagine it happening again. (I know Mosconi won some world title like 10 times in the 30s-40s - I think that's apples to oranges.) Possible sure, but very unlikely.
I believe the 626 - - if that is the record high run in practice - - can be beaten again. Will it? I don't know. I think pool is not much different than other sports in this regard, as Stu has alluded to. The four minute mile, once thought sacred, was beaten in the 1950s and has since been beaten about 1500 times since then. So how fast can Usain Bolt, the fastest man alive, run a mile? He's reportedly never run a mile. Why would he? It's not what he competes at.
How many balls could Rempe, Miz, Sigel, West, etc. have run in their prime? How many can Filler, Hohmann, or Feijen run today? Enough to win. Just like Bolt just had to run faster than the guy behind him over the distance he was competing at. It would be ludicrous if he just kept going for a mile afterward.
Unfortunately, with 14.1 relegated to nothing more than a practice game except for one or two events a year, or even fewer than that even without COVID, the concept of excellent play will probably be focused on high runs because tournament wins are becoming harder and harder to come by in the game.
It's a shame, because 14.1 can provide some great drama if it's a close match. If two players are playing well and trading 40-50 ball runs, it's very exciting watching the last few racks knowing whoever is as the table can end it, while the guy in the chair can do the exact same thing. It's like an extended hill-hill match. Separately, there's always the chance of a player starting with a big run, only to lose the match if the other player runs out, or has better table management skills. Everyone likes to watch the 100+ ball runs, but I always thought 14.1 really provides excitement if it's contested, more so than the rotation games. Perhaps I'm in the minority here, but those contested games are much more exciting than a guy running balls for half a day. 14.1 competition on the other hand, can be extremely entertaining.