As long as i get to be the frog
The 4e DM's guide had great advice on house rules. To paraphrase it was: "Clearly Identify what it is you are trying to change with the house rule and why it needs changing. Will the house rule achieve your goal?"
Open up choices that are being restricted for no good reason.
I could be reading too much into OP's post, but it reads to me like he'd like to remove skill choice restrictions so that any class can specialize in any skill - presumably because he has a class idea that would need a different skill.
I think that's a decent summary. Though I do think toward the end you are presuming too much.
If I was a DM for a player asking this, I would instead make it an exceptional case if the player can give me a sufficiently compelling backstory to justify them being proficient with a few skills that they don't normally have. Then I'd roll it into a new background.
Why make him jump through hoops to play what he wants when you and I both know that whatever skills he ends up choosing isn't going to hurt anything.