My initial thought with the limitation is carts - obviously the course only has so many, and if too many people check-in early and load their stuff up it can affect golfers who have an earlier time.I like to show up about an hour before. I won't check in right away though, just get some practice and check in closer to 30 minutes before. I feel like they should let you check in whenever, understanding your tee time is still your tee time. I don't understand why they would not allow that, unless their system can't handle it. who knows though.
Personally I think if you check in more than 30 minutes early you don't have an expectation to be putting your clubs immediately onto a cart anyway, but that's me.