It's all of the above. Some players opt not to play if they feel they need rest/have family matters to attend to. Federations don't try to entice or even talk players into changing their minds because they don't think it matters. And clubs, naturally, never have any interest in the success of NT. But they are not as big of a factor as you make it seem. I find it very unlikely that Polish or the 3 leading Hungarian teams allowed players A and B go but not players C and D. Something like MAC have 5 players on this Hungarian team but told Bodo you aren't going? Unlikely. Just like in Lithuania's case, this seems to be mostly between the player and the federation.
Well anyway, it seems to be working for both Poland and Hungary.
Come on, Brahmanis only came back to Latvia because he was starting to slow down due to age. Let's face it, players play in Latvia if they have nowhere else to. In Poland, that's not necessarily the case. Same way Polish clubs are able to afford some decent C-grade imports like Teddy Da Costa or Gleb Klimenko. Even numerous Latvian guys, someone like Biezais was a great import.
But sure, never said your point is wrong in general. Just that Polish league is ahead of Latvian any way you slice it and some players at the top of it are not too bad.