It's really on the team to manage their workloads the rest of the time. Maybe ease them in a little in April, or just include the WBC in their "live" innings/pitch count for the season. On the other hand some of them may be sharper.
These kind of tournaments are a tough sell in general. I don't think Americans watch the world championships in basketball or the world cup of hockey (which just came back) either. Olympics would draw more interest. What they should really do is make baseball part of the Winter Olympics (it would just have to be in a different region) and hockey part of the summer Olympics (no problem there, indoors, though ice quality might not be great) to solve the problem of season interruption.
As for the end of the Cold War, I agree about that, and it doesn't bother me. Sports rivalries and tribalism/nationalism are the same impulse, just much healthier to express in sports. It's more fun to watch the Phillies beat the Mets or even the Yankees (not a rival but a hated Goliath) and it was more fun for the US to take on the USSR and it's still more fun for Canadians to beat the US in hockey than it is to beat Sweden (and Sweden is better).
That said, US and Russia should still be a pretty big rivalry.