I'm kind of mixed between the idea of closed species, but I mainly lean more towards having a dislike for them. Most of the time, they aren't really that original, just being a mash up of two or more different creatures/objects, or just being a existing species (ex. humanoid/mlp cs) with some added traits and lore to make them stand out. Granted, I've seen a couple of closed species that are quite unique and even have interesting/cool lore/backstories to them, but they were always more obscure or not very popular.
Another one that most people can agree on is that they can cost quite a fortune, especially with very popular closed species. Depending on the price, I see it as being a waste of money just to gain permission to use a picture someone drew and/or rights to the species it's centered around on. If you're able to afford it, then by all means go ahead, I am happy for you. But I personally don't really like the idea of it.
Also this is more of a personal thing, but with a few how quick people are to claim, not leaving the slower people who may be interested in getting one a chance.
I can agree on the whole "strict rules" thing, if there isn't a lot and are easy to follow, then I'll happily follow them. But if they heavily limit you, then that's a good reason for me to turn around and walk away. It's even worse when it can lead to whatever you own getting revoked. It's quite a scummy thing to do in my eyes in a few circumstances, such as if it's one you invested actual, REAL money into. Once they buy it, you do not have the rights legally to take it back, unless they explicitly agree they are fine with it, or you give them a refund.