The first 2 broodys I had I let hatch eggs, both went broody again once their first group of chicks was weaned and I let one hatch a few more eggs. The other I just let go through the motions of broodiness minus the eggs/chicks. I let a 3rd hen go broody and left her to her own devices as well. When left to be broody they eventually give up but it seems to take 4-5 weeks of sitting as opposed to the 3 weeks of sitting on and hatching fertile eggs. Of course it is natural for a hen to go broody but after a while it can affect their health, even more so if they are repeat offenders. Some can be so persistently broody that they become emaciated.
Should I have broken them of their broodiness rather than letting them sit? Yes I probably should have but I didn't have a solid way of doing it. You want to pen them up but not in a particularly comfortable spot or they will just sit in a quiet corner and continue being broody. A lot of people break them from being broody in a dog kennel, keeping them there for a few days and then returning them to the flock.