It very much is a cousin of the broken window fallacy.
Bastiat's original point of the Parable of the Broken Window could be summed up by the aphorism "not everything that counts can be counted, and not everything that can be counted counts". It's a caution to society to avoid relying too much on metrics, and to realize that sometimes positive metrics obscure actual negative outcomes in society.
It's very similar to the practice of startups funded by the same VC to all buy each others' products, regardless of whether they need them or not. At the end of the day, it's still the same pool of money, it has largely come around, little true economic value has been created: but large amounts of revenue has been booked, and this revenue can be used to attract other unsuspecting investors who look only at the metrics.
Or to the childcare paradox and the "Two Income Trap" identified by Elizabeth Warren. Start with a society of 1-income families, where one parent stays home to raise the kids and the other works. Now the other parent goes back to work. They now need childcare to look after the kids, and often a cleaner, gardener, meals out, etc. to manage the housework, very frequently taking up the whole income of the second parent. GDP has gone up tremendously through this arrangement: you add the second parent's salary to the national income, and then you also the cost of childcare, housework, gardening, all of those formerly-unpaid tasks that are now taxable transactions. But the net real result is that the kids are raised by someone other than their parents, and the household stuff is put away in places that the parents probably would not have chosen themselves.
Regardless, society does look at the metrics, and usually weights them heavier than qualitative outcomes they represent, sometimes resulting in absurdly non-optimal situations.