Did anyone ever think to give Voldemort a little TLC instead of hunting him down?

Well...the fact that as you were trying to capture him he would be trying to Avada Kedavra your **** kind of would put a kibash on that plan. Putting somebody in an asylum only works if you are able to capture them. I'm sure that if early on in his reign of terror Voldemort had been captured then he would have been sentenced to life in Azkaban.