This assumes that no-one in 2017 had heard of Metcalfe's Law and...

This assumes that no-one in 2017 had heard of Metcalfe's Law and that the valuation in 2017 didn't have expectations of growth already priced in. Given TNY was trading at around 30x revenues and was losing money back in 2017 I'm not sure that's true.

I'm not a sceptic on TNY - quite the reverse - but I also think Metcalfe's Law is also inappropriate here. It's not like photos of your kids are a many-to-many type deal where the network is 100x as good if there are 10x as many users on it. That might be true if it's a marketplace or a community of some sort where we prize many-to-many type relationships, but I don't think 4x as many users signing up is going to make someone think "hey, I'm going to share my kid's photos with 4x as many people now".