Will taking falls on a rope wear it out?
No. Ropes wear out from being abraded (such as running over an edge), not from stretching (as in a fall).
If you're worried about taking more falls than a rope is "rated" for, you're misinterpreting the UIAA fall rating. The UIAA fall rating is simply a way of measuring rope durability and refers to a very contrived testing condition that could never happen in real life. All ropes that are certified for climbing have a fall rating that is acceptable for anyone. You should ignore this number.