Let them? I'd have a hard time not allowing them...I sleep with multiple fans and with the AC on as I live in Texas and like it cold inside, and they love to sleep on my bed! There's nothing like snuggling up with my Maine Coons.
Cucumella used to JOIN me in bed but lately she goes to bed AHEAD of me and waits impatiently. In the morning she lets me know it is time to get up by licking my face, tapping on my chest with her paws, pushing her head against my throat and making throat noises which resemblent from a bird.
CoCo, won't leave my bedroom, gets real excited. She runs around continuously meowing. Peaches jumps on and will growl whenever one of my cats jumps on. She sleeps on my legs and will growl if I squirm. I have 4
Most nights we have at least one on the bed with us.
I like it depending on who it is and where they sleep. Snickers weighs a ton and likes to sleep on my legs, which I don't like, but it's OK as long as he's on DH's side of the bed. Cinder and Laelia like to sleep by our feet, for a quick get-away. Toothless likes to cuddle up by me, which I LOVE.
I've never heard that sleeping with cats causes health problems, and I'm not worried about it. Being alive causes health problems...
I like to think they sleep with us because they love us, but the truth is probably because we have a waterbed so it's always nice and warm.