Maybe it's a mindset difference, but some of the arguments come across weird.
I totally get wanting to limit character applications if your argument is limited staff time, and you don't want to spend that time on approving characters for people.
But I'm kinda scratching my head at arguments like, to help you keep pace, or teach you how to manage your time, or because you think the dopamine from making a new character is unhealthy. That sounds patronising.
Keeping pace and managing time are personal skills to develop, not to have dictated to you by animanga roleplay site staff members. I certainly don't do roleplaying so I can have someone tell me I can't have another character because you think I need to learn how to efficiently spend my time.
Not everything has to be a race of perfect efficiency, and wasting your own time on your own terms shouldn't be a problem at all. If you, as staff, think approving someone's characters is a waste of your time, you probably shouldn't be staff. (Alternatively, learn how to efficiently use your time to approve characters.)
Likewise for the idea that it's unhealthy to move on from one character to the next. It's great if you're able to maintain focus on one thing and that keeps you happy, but other people suffer shorter attention spans and need to be constantly challenged with something new to maintain that spark. It's fine if you think that's unhealthy, but let's not put ourselves in the seat of mental health professionals and make health decisions for people.
I don't even write many characters, often sticking to one main character and at best two extra characters. That has mostly to do with that the first character will be written to fit many threads, and if I find there's stories I can't tell with that main character, I'll add another one that has a specific other direction to go in. Because those are necessarily more limited in scope, the number of threads I'll write with them will also be considerably less.
The way I see it, if you're concerned with the time it takes to approve a character, maybe try to streamline the approval process to make it easier on staff members and limit the time spent on that. For example, you could ask people to answer two questions in the biography section: "Who was this character before they arrived at location X?" and "What motivated character to move to location X?"
Then you could either ask people to keep the biography strictly to those answers, or as staff just skim the biography to find the answers to those questions and consider mainly those.
"But Traveller, I'm worried they'll write things that break the setting!" Then you either need to define your setting better so people know where the limits are,
or you need to let go a bit and accept that, once you throw other writers into the mix, some stuff may need to bend a little.
It's not like staff are infallible: I've seen staff members introduce characters that conflict with site lore or that don't make sense internally. Like the time I saw an admin introduce a character that was homeschooled in their home country, not knowing that homeschooling in said country is a crime.
Addendum: If you want to limit characters, then please let it be for logistical reasons like limited staff time, or because there are limited slots for specific roles, or because lore-wise there shouldn't
be that many people. Don't use character limitations because you fancy yourself a head master here to teach people lessons through limitation.