The walkthrough (included with the game) says 10 spots with individual 20% chance daily. I check once a week and average 6-8.
Doggo was never meant to be a wardog, more of a medium-size working dog or pet. He was added because players wanted a more-or-less permanent companion. He's already been upgraded a couple of times. The first version didn't respawn and you had to buy another if it died; highlighting ingredients was also added.
He's not required for anything that I'm aware of, you don't have to get him if you don't think he's worth it.

Doggo does just fine for me. He's effectively bonus attacks in fights. I've lost track of how many times he scored the last few HP to put down an opponent, or took a hit instead of me.
A bigger dog could be added to the game, costing more. So could better gear for dogs. (Or maybe you have to commission it, or make it yourself...) But the dev is focused on finishing the Main storyline and then some aftermath/cleanup/etc. before the RPGM editor hits the wall. I suspect dog buffs aren't a high priority just now.