And he didn’t miss a paycheck from Bayern in the four weeks he played for England in the Euro, because he’s got a contract with them not only for the seasons, but for the whole year round (as most players have).
I think stadium availability played a part. A lot of the teams played in NFL stadia. Not so much anymore, there’s been a lot of soccer specific stadia built in the last couple of decades. But when the league started, there were practically none.
As a high intensity sport, playing in the mild European winter months is vastly preferable to playing in the summer heat. Most of Europe doesn’t get the brutal winters you find in much of the US.
And those that do, either play in the summer (eg Norway) or have a winter break (the Russian league has a break from mid December to the end of Feb.
Historically the European competitions have also taken a winter break but I notice for next season that is not the case. I do not know if arrangements have been made for if a team like Bodo progresses that far.
For what it is worth
FIFA has rules that teams generally should release a player that is called up by the national team , and the player is expected to accept ( although I can’t imagine many declining)
This link to the European Club Association has a pdf describing some of the issues that came up due to extensions of the time that the players should be made available .
Also FIFA apparently compensates the clubs for World Cup appearances.