That's an interesting idea. However, while I agree that theoretically pitchers should be able to warm up safely beforehand, it feels like there'd be a lot of pushback on that idea for safety reasons. That said, I do agree that there should be a way to get out of the 3 hitter minimum and whatever "punishment" that incurs should apply whether an injury occurs or not to avoid teams faking injuries. So at that point it's a matter of making sure 1.) the "punishment" is harsh enough to avoid teams just routinely taking the hit, and 2.) the punishment isn't unfairly harsh to pitchers that actually have an injury.

With them rolling this out in the minors for a year first, it'll be interesting to see if they decide a tweak like this is needed before bringing it to the majors. Here are a couple ideas I've had or heard on the board in regards to a pitcher not reaching the 3 hitter minimum:

1.) Zurch's Goalie Rule - No mound warmup allowed for incoming pitcher.

The more I think about this the more I like it. The obvious caveat is that people will be worried that managers won't have a reliever ready to go and they'll risk further injury by bringing a guy in cold. However, if the real goal of the 3 hitter minimum is to reduce down time, this accomplishes that in several ways: 1.) encourages teams to reduce pitching changes, 2.) encourages managers to make sure relievers are ready to go right away when needed, 3.) reduces commercial breaks caused by pitching changes.

2.) Forced Injury List - If you take a pitcher out early, he must go on the IL.

I think this is a viable possibility as long as it's not a full IL stint, which would be too harsh in some real injury situations. Perhaps a 3-day ineligible time period would be more appropriate. If a player truly tweaked something, this would be a reasonable amount of time to let them recover anyways.

3.) Just Enforce the Rule - If you want to take a pitcher out early, too bad, you just have to walk however many batters needed to fill the minimum.

This could also just be the fallback option for a manager anyways if he wants to avoid whatever punishment is in place for not meeting the minimum batter requirement. Since you don't even need to pitch to a batter to issue an intentional walk, it doesn't risk further injury to the current pitcher and it also doesn't add as much "dead" time as having him actually pitch to additional batters. Also, while this is a little bit of a stretch, I'd argue while it puts the team in a bigger jam and may increase scoring in the game, adding extra runners to the basepaths actually creates more out possibilities for the next pitcher and may actually increase the likelihood of them getting an out or a doubleplay to end the inning sooner than if the walks weren't enforced.

I find it really interesting to think about, however, I also wonder if this rule is just being proposed as a future bargaining chip for negotiations in the next CBA.