Your point stands if PW is available from the very start of the game.
I will note that if I go forward with PW as a "primary" mechanic, I would definately have it available earlier in the game.
So a number of people are worried about having to build PWs more often and for them to be "boring", and there is some fair concern there. Obviously a simple solution would be to apply -1 unhappiness to more buildings, like your universities, custom houses, etc. Now the issue with that can be (which the current system tried to resolve) is the notion that a bunch of buildings could make happiness "too easy". With the current system, because of the way yields work... buildings tend to "obsolete" over time. That market that once removed an unhappiness for poverty effectively stops doing that as your needs rise.
There is a way to replicate that. We could do something like this: Library: -1 unhappiness in any City under 15 pop.
This effectively sets a self obsoleting mechanic. As cities start to grow up, those old buildings just don't do anything for the people anymore, and they lose their benefit. This allows some of the infrastructure race that the main system provides, but again in a much clearer, understandable way.