Lots of cards not available in the Campaign. Bug or intended feature?

I've been playing through the first 4 campaigns (Base game + Fire) and noticed that during the Home City phase where I pick new cards for my deck, a suspiciously large number of cards never become available.

I cannot remember if this was always the case. The new Tech Tree system is very unintuitive in regards to the conditions for each card. I don't think it tells you what Age the card becomes available and how many times it can be sent. You have to invest a point in it and go to the deck builder to see those details.

I also don't have a clue whether my town is just not a high enough level to unlock those cards yet, or are they not meant to be used in that campaign at all?

I was under the impression that the campaigns use custom civs. Are they actually using the tech trees of existing civs?