I find it very frustrating when I'm working on a project and I go to pets for breeding only to find the female I need to breed with has been used by someone <just because>. I don't mind if someone is working on a project and they beat me to it but when someone is just doing it to do it is frustrating.
This kind of came to a head for me today. I was looking for a female with a specific trait and was available. But by the time I clicked on her someone had beaten me to it. yeah, I know this happens, and is part of the game. But when I went to see what this person was working on I couldn't believe it. They have ONE stable with 4 tabs that are almost completely filled yet they have 11 pages of babies in their hatchery. I then looked up released pets. Yeah 1530 and the person has only been here about a year. This is to much! There needs to be a way to regulate this. Maybe there should be something like you're only allowed so much hatchery space per stable space or something else. I know it will be difficult and will impact people like myself that have big projects but this is silly for someone to just breed everything they can "just because"

As much as I would like to see a limited hatchery list, I see a few problems with it.

Someone that is just randomly breeding pets is paying the same breeding fee/cool down period/etc. So it might be problematic to try and give restrictions, because technically they have the same rights to breed pets as people with projects.

Next is hatchery space. I don't feel like they should limit hatchery space, just because some people are 'misusing' it (which is subjective because to them it might be alright). When. I was really active I'd have TONS of hatchery tabs, even though I didn't keep anything. I would release, sell or give away a lot of those pets. Since pets live in your hatchery for about a month, you can potentially have 450 pets if you bred 15 a day for 30 days. Divide by 25 pets per page, and that's already 18 pages. That's easily plausible with a couple of projects that your mass producing egglings..

Another thing is, I don't think it should be dependent on how many pets they release, even if those pets don't have 'value'. I know people that release mass amounts of failed project pets. So where is the difference of project vs just because pets.

Overall, I see where this would be a good idea, but I'm not sure how well it would work. It's hard to draw a line between where things would be even for everyone.