But soccer/football stops dead all the time for the World Cup, and also for friendlies (just got my email ad for Sunderland-Wrexham here in August as I'm sure you did too). Three times a year! MLS just finally took steps to adjust its own calendar to keep up.
And hockey is going to have a World Cup in 2028 (in February) and had the Four Nations which shut down the league for 12 days last year. They're probably going to keep doing both (or one or the other). Women's hockey also shuts down twice per season (for the Rivalry Series and either the Olympics or the Worlds, since unlike the NHL all of their players go to the latter).
For sure baseball's calendar and weather needs make it more complicated but clearly MLB wants the $$$ and marketing. They could probably care less about the Olympics since they don't benefit from that directly but if it suits them to make the players happy and they can get a piece of the action it would probably happen. And then you have the WBC in the even-numbered non-Olympic year (you do one or the other every two years not every year).Andy's idea for a much smaller tournament also makes sense, and would put it on the same rough timeline as the Olympics where the WBC is currently not.