I did wait it out once, so here is the honest version of that option.
She sat for about twenty-three days — roughly the length of a real hatch, which is the point, the clock is built in. She came off thin, stopped laying for a further six weeks or so while she recovered and moulted, and by the time she was laying again the season had largely gone.
Nothing terrible happened. But I would not choose it again for a bird that is already pale at day nine, and I would never choose it in hot weather, where a hen who barely leaves the box and barely drinks is taking a real risk.
One thing I would say in defence of waiting: if you actually want chicks at some point, a reliably broody hen is an asset and repeatedly breaking her is working against the only free incubator you will ever own. Some breeds do this every year and it is not a fault. But that is a plan you make in advance, not a reason to leave a thin bird sitting on nothing in August.