The value add is that you can have decent confidence the product isn't so crappy that the brand is unwilling to put their name on it. Presumably Walmart, Harbor Freight, Amazon, whoever at least got a test batch of the product and made sure it actually worked before ordering millions of them. The consumer can just buy the widget at a slight markup for $1.99 and know it will work instead of going on Ebay or Alibaba and buying direct from exporters and wondering whether they should get varieties A, B or C for $1.59, $1.69 or $1.79.
If it's an electronics part, I would also like the FCC submission numbers, UL submission numbers, etc. For every regulatory agency in which a filing was made, I would like to be able to see those filings.
Those filings should also count as the advertised product specification. If they change chips or designs outside of the specified list I should be able to return the product for it being different than the listed item.
In some of these categories it is basically heaps of 3rd parties slapping logos on the same stuff and the winner is whoever best games the reviews for search rankings. They are now annoyed that in some cases Amazon decides that there is no winner.
There are considerations people have that are above and beyond the purely utilitarian.
In some cases the private label even uses the same manufacturers, the people producing the product still get paid in the end.