Does this 7 Wonders analysis make any sense?
The analysis is technically correct, but practically kind of wrong.

Every choice of card in 7 Wonders comes with an opportunity cost, which is to say, "What are you giving up by choosing this card instead?"

It is true that the brown resource cards in Age 2 give you access to twice as many resources as their Age 1 counterparts, for the cost of a single coin which is usually not huge as far as things go. However, if you decide that this means you should ignore the brown cards in Age 1 and just wait until Age 2 to get them, then:


You run the risk of never getting the resources you will need, especially if your opponents are paying attention and carefully deprive you of key cards.
You spend less of Age 2 building more useful cards (e.g. Science and Military cards, especially the ones that enable you to build stuff in Age 3).
You potentially have to spend more coins building things in Age 1, if you're relying on neighbours to provide the resources.
Conversely, your neighbours will not be buying resources from you, denying you a source of income.


It's easy to be flippant and say "It all depends on the cards", but really that's the point - 7 Wonders is a game of making lots of decisions, and there is rarely a singular strategy that you can follow blindly to success.