Could say the same for imperial China. Lots of concubines, lots of kids.

I believe they used to bury the (living) concubines with their deceased emperor to solve that potential issue at some point, but every time there were multiple brothers, it usually ended in blood.

Whether it was the spoiled "I'm more deserving of the throne" or "oh shit, I'm a threat and he'll try to kill me anyway so I might as well rebel", every succession left quite a lot of familal corpses behind.

It's like every time one dude fucks around, everyone else gets to find out...

What's the last bit? They isolated them from society so they don't have to get murdered? But what's stopping one of the one's that are not the new sultan to murder the sultan and become sultan himself?