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.

Web References

1. https://outdoors.stackexchange.com/questions/508/climbing-rope-is-rated-to-x-uiaa-falls-what-is-a-uiaa-fall
2. https://camcamnut.com/guides/what-does-uiaa-falls-actually-mean