Hi Andy

There doesn’t seem a lot of point in smoothing out the lawn only to let the dog rip up up all over again!

I suggest you have two choices:
Enjoy the dog, let it run around and play and look after the lawn as best you can. Aerate and feed as you’re doing but also grow it longer which makes it wear well and perhaps a sprinkle of seed in damaged areas.

OR perhaps you haven’t thought of more logical solutions....
a/ Put the dog on a leash
b/ Don’t let the dog on the lawn
c/ Trim its nails
d/ Get a tortoise instead!

Happy New Year