No, it's not a good move. This has nothing to do with backyard breeding.
First it's any combination of companion animals, not seven of any given animal. Pretty much anybody who lives on a farm is going to have to get a permit. Also notice there is no mention of how much the permit costs, nor any LIMIT to how much it will be allowed to cost. And what's a "ridiculous" number of dogs? Seven is a ridiculous number of dogs? Seven is more than I'd like to have, but there are and have been members on this forum with that many and even more, and they all get great care. And again, it's not a number of ONE animal - if you have three dogs and four cats you would need the permit.
Secondly, if you are, say, the kind of backyard breeder who is pumping out litter after litter and you never get your pets the proper vet care so you're turning a profit, paying a potentially large amount for a permit will be no big deal, so it's not going to stop them.
It WILL, however, be a financial burden for the small hobby breeder who breeds maybe once or twice a year if that. As an example, Auggie's breeder hasn't had a litter in three years, but she would definitely need the permit since she lives on a farm and has dogs, cats, two chickens, a donkey, and a small flock of sheep.
Furthermore, the kind of people who break the law will continue to break the law, so it won't stop THEM either. They won't apply for the permit until they get caught.
Finally the law is intended to be about animal hoarding, and has nothing to do with breeding. (That was a completely separate bill that has been defeated.) For one thing hoarding is based on an illness, so you can't legislate somebody out of an illness, and it's not going to HELP them to try and legislate or fine them for it. For another the law as written was just fine for the intended purpose, because it focused on the quality of life for the animals and was not worried about trying to set a number on how many animals any given person can or can't have before they have to buy a permit for the government.