Would it be bad to put my indoor cat outside? Don't want to rehome him, but am at my wits end

Hi. I got my first cat a few years ago. He was originally a street cat, saved by a shelter and I adopted him. The shelter kept them indoors and said we should too. And I also generally don't believe in sticking your cats outside all day with all the dangers. Anyway, he has a very affectionate side which I love. But his, how do I gently put it.. less appealing side has always taken over. He wants to go outside, and escaped a few times. Since his escapes, I guess he tasted the fresh air and wants more because his behaviour worsened since. A few things:

He is constantly yowling at the door and is very dominant to my other cats. He also loves to break things as he is frustrated he can't go outside. He will find a way to open every door and when he does he breaks stuff inside that room. I can barely decorate my house and it's lowkey depressing. He's always jumping on doors to try and get outside. Most of my evenings are spent correcting his behaviour. And yes, they have multiple big litter boxes all kept clean, loads of toys (he has 0 interest in them or in interactive play), has been checked by the vet and is healthy as a fiddle, always plenty of food and water.

My other cats are now starting to copy his bad behaviour and I genuinly am not able to handle more than just him. Sometimed I just want to give in and put him outside instead of constantly being annoyed. And yes, I have tried multiple ways of redirecting his behavior. I'm not looking for comments like "try feliway" or such because I have tried. I am however wondering if it would be alright to let him go outside.. maybe he would be happier that way.