Tom Tango analyzes the new pickoff rule (and all the other rules, too) as he tries to develop the game theory used by batters and pitchers to decide when to throw to the base and when to run. A couple of things stood out for me. First of all, the problem of teams gaming/abusing rules came into play. Tango uses an example from ice hockey:

In the NHL, coaches would sometimes delay games as a tactic, as allowed by rule. This was done by swapping goalies. Swapping goalies was reserved for two things, in its history: poor play of the goalie and injury to goalie. And, like with relievers entering a game, as a courtesy, the new goalie got to warm up. Until one coach decided to swap goalies back and forth to get a defacto timeout. The referees would always allow the goalie warmup each time, though it became apparent quickly that this was getting out of hand. The NHL put a stop to it by eliminating ALL goalie warmups. If you can’t police yourself, then the league will came in with a zero-tolerance policy.

TangoTiger.com

Pitchers using pickoffs as a delaying tactic could get out of hand. I often wondered if pitchers who executed multiple pick-off attempts were simply afraid to pitch to the batter.

Second, STATS, Inc. found in the early 1990s that the first pick-off attempt was the one that mattered, and that was true in the 2010s as well:

Let’s describe all this in terms of run per 1000 opportunities. In the 2010-2022 time period, the baserunner was at almost exactly 0 runs (-0.1 runs), when no prior pickoff was attempted. He was at -0.6 runs with at least one prior pickoff. So, the pickoffs worked for the pitcher. 

We had known for three decades that throws to first base after an initial attempt were a time waster. While the pitch clock rule sped up the game tremendously, reigning in pick-off attempts helped a good bit also.

There is so much more excellent analysis in the article, I hope you read the whole thing.