The example that started this is someone taking care of an elderly person themselves vs working overtime and paying someone to do so. Simply by working overtime for a company, this person created economic value, likely higher than of their own wage. Second, other economic agents received payment in exchange for services, so this also increased our productive output. In both sides of this operation, taxes were paid, and the country is therefore wealthier in both a fiscal and economic sense.

I think the confusion here is because it seems odd that taking care of your parents by yourself is not considered productive unless you exchange money for it. GDP is an imperfect measure, and by definition does not take into account such voluntary/unpaid activities.