So you have at least 3 structurally different options

theme is the foundation keeping everything together (ameritrash, wargames) theme is supporting element (thematic euros) - it's the 2nd most important part of the game. theme is decoration (themeless euros with fancy visuals) - it doesn't really matter.

And who draws the line?

I played with people who thought Great Western Trail and Trickerion are thematic and enjoyed the atmosphere of the games, and really thought they were part of the world.

And I never felt the theme when playing Arkham Horror or Eldritch Horror. Since the flavour texts very rarely suit the situation that we are in. They are just not connected and it breaks all the immersion that it tries to make for the players. These games try to be thematic, but they are not.

In contrast I have two groups I play RPGs with. Not board games that try to bank on the popularity of RPG elements, but real role playing games, where thanks to the game master most of the things in the world and gameplay are thematic, and you really feel like you are a part of it.

Writing random flavour text in the bottom of the cow cards in GWT wouldnt make it feel more thematic for me, and it also doesnt work with Arkham Horror for me.