" There is no scope for difference between a “big corporate” CA and a “small politically active” CA because the work they do is so mechanical, auditable and predictable."
There is room for a politically-active CA like there is for anything else. In each market, there's players that get business for doing better things for privacy, being eco-friendly, being more inclusive, etc. Things that get business from vote with your wallet types. My idea, inspired by Praxis doing Mondex's CA, was a non-profit or public-benefit company that had built into its charter and legal agreements many protections for the customers in a country without secret laws/courts like U.S. Patriot Act. The CA would also be mandated to use high-security approaches for everything it did instead of just HSM's. They might also provide services like digital notary.
In short, I can imagine more trustworthy and innovative CA's being made. I'd easily pay one like that over the rest. I'm sure there's some number of people and businesses out there that think the same way. I wouldn't try it as main business, though, since market is too cut-throat. My idea was a company like Mozilla would try it to see what happens. Let's Encrypt confirmed the non-profit, public-benefit part being feasible.