Your original claim was, and I quote, "the whole system was a very carefully calculated pyramid of power and privilege".

You report that the Puritans were intolerant but the bottom line is that the greatest source of power, the Constitution, prevented them from exerting their intolerance.

Why?

It's so easy. Drop a line in about personal worship of God Almighty to build your relationship with Him being the only thing that's protected and you can discriminate all you want against Catholics (no Papal power) and Deists (no personal relationship), and a lot of Quaker practices too (they don't demand these things).

It's so easy.

Why didn't they do it?

Don't point at ancillary facts about the prejudices of some colonists, as if this demonstrates that their will must undeniably have been implemented. Explain why when it was so incredibly easy to enshrine those prejudices that they weren't.