That's what I would do. It's not worth patching; I've tried fixing those doors.
Ex-GF was renting a trailer. Boy ran full blast down the hall and smacked into the hollow door. I patched it. Next day he bumped into it again and perfectly knocked out the new filling. He didn't hit hard enough to break the door- had it not been patched- just bumped it and knocked the filling out. I decided it wasn't worth fixing at that point. Same would probably happen if you patched it and it hit the door stop again.
Just be glad its not like the doors I have in the house. The doors are the originals from 1946. A few are broken, and the closest match I can find would cost about $300 a pop to have sent to me. Apparently, very few companies make solid wood- actual 1.75" thick wood, not solid core- anymore.