I don't know if this line of argument is going to be very productive.
Civ game mechanics are an extreme abstraction of real life economics. This is just one thing the game does not represent accurately at all, because it is more concerned with being a functioning game in this respect. By extension, the relationship between the real life effects of forms of government and society and the effect of the corresponding civics will be equally abstract. It can't work any other way.
It's better to look at civics being "themed" after what inspired them, to make their effects roughly intuitive. I've also tried to group the effects of related civics in ways that make them synergize and imply an overall strategy, i.e. capitalism = cottage economy, socialism = specialist economy, totalitarianism = espionage economy.
Of course there are limitations and you will always find counters in the varied list of historical examples.
I tentatively agree that the religious column is weak right now. I wouldn't necessarily say inaccurate, but in general it's really just an uninteresting choice: "so we have a religion now, do we want more buildings, units or GP?". But I think we can live with it until I have put things in place to replace it. Extra science for Secularism is the least of its issues in my opinion though.