What's been your experience with a cat door?

I can answer part of your question. I have a doggie door and there is a solid door that slides from the top to cover the flap when you want to “lock” it, so there is no way a pet can unlock it, or actually slide it up, to escape.
Also, I have never had any other creatures come in while it was in use.

Yes, yes and no.

Yes, very successful, but each cats learning curve is different. My old guy that passed away in 2010 took 6 months to learn to use it. I installed it when he was 10 and he was slow to master it after never using one before.
The new kids in the last 3 years mastered it almost instantly and Myles is such a tank he has to go through slowly or he gets hung up. haha

My little Siamese is a like a bullet…whoosh in & out.
Yes, I had some issues with the Raccoons a few summers ago, but…mine exits via a back kitchen door into the garage, so, once the garage is closed up for the night, no more critters. The cats access their litter boxes in the garage night and day.
Mine has a panel that slides in to form a solid barrier so there is no chance of any escape.

Otherwise it is just the flap with the magnetized strip that seals.
No drafts and closes snugly.
I highly recommend them, they are wonderful!

P.S. The unwelcome guests only show up at night, usually after 9–10 p.m. so, as long as Milo is in for the night before curfew you should keep the other party animals out.

Well, I find that if I can get my head through, I can usually squeeze the rest of me through there as well.

No personal experience but i do know that there are cat doors which will only open for a special collar attachment worn by your cat if you’re concerned about other critters or stray pets pets belonging to others.