I totally agree. Permitting a broody-prone hen to go broody in a serial manner is not a good idea and, as you have already indicated, it's not doing what's best for her. I say that in the spirit of helpfulness and for two other reasons.
The first is that it's a waste of the resources of a broody hen to permit her to brood an empty nest or eggs that will never hatch.
The second is it's an assault on the health of your pet hen to allow serial broodiness as oldhen has pointed out. Whether we keep chickens for livestock or as pets, it's incumbent on us to give them proper care to maximize their health.
Breaking a broody is as simple as installing her in an open mesh bottom cage (so cooling air can circulate under her and interrupt the broody hormones) with food and water for approximately three days. She will emerge good as new and won't waste the next month or longer sitting in a nest running down her health and having nothing to show for it.