Let me repeat that: a required skill, going with class-thematic background that already grants it, means that instead of picking from the class list of appropriate skills, the player can instead pick from any skill, which includes a lot that are less appropriate.
You can already run into this in 5E, since officially you pick class skills first, and then if you pick a class-thematic background, it's very easy to double up on skills and wind up picking from the full list. Plus you can customize backgrounds to include whatever skills you want (you have to justify it somehow as part of your "background," but it's usually not too hard). So the reality is that characters pick 2-4 class skills plus 2 skills from the whole list, and I don't see how things are really any different if you also give some classes a free skill or two. It would be similar to playing a race that grants that skill.