I think that every hen has her own component of broodiness. Some have little to no amount, and will never go broody. Some may do it only once or twice in their lifetimes. Others will regularly & routinely go broody their whole lives.
Therefore, some hens will be easier to break of their broodiness than others. With some, all it takes is lifting her off the nest & putting her out in the yard with her pals. Others need to be confined in the wire-bottomed cages for days to change their mood.
I don't think it would kill a hen to let her stay broody for months at a time, but I also don't think it's really best for her. Certainly she's getting a rest on the nest, she isn't depleting herself by making & laying eggs, but she's in a situation that's only meant to be temporary. I've had hens that set eggs for 3 weeks only to have none hatch, so I re-set her with fresh eggs for another 3 weeks. The hens would be fine, but I'd be hesitant to continue doing that more than 8 weeks or so.
If you have a hen that is a determined broody, I think it's kindest to let her set rather than continually trying to bust her broodiness. Find a BYCer or other chickeneer in your area who has eggs they'd like to have incubated. Your hen can incubate other kinds of eggs too, duck, turkey, goose, guinea, etc. Or just give her 3-4 eggs to set, enough to satisfy her urges. Find someone willing to take any cockerel or surplus pullet chicks. You can have fun watching your hen tend her chickies for several weeks or more before you have to re-home the extras. Or just swap your broody hen for a different one who is less family- and more career-minded.