Yes, I want more ways to impact the levels of different religions within my empire. I want the ability to close borders to "foreign preachers"-even if I am friendly with the Civ that is sending them. I want Social Policies that impact on the ease/difficulty of how religions can be spread-both actively & passively. That would be the "next big thing" for me.
If I can make a more general comment on this...
Civ VI's designers made a basic mistake with the entire Civics Tree/Social Policy system: they made it linear, like the Tech Tree.
Ironically, at the same time they gave the Tech Tree several 'dead end' Technologies which reduced the linearity of Technology.
In fact, Civics and Social Policy are both hard to change (much harder than the game implies) and distinctly Non-Linear. If they were linear, then all 'Civilizations' in the world today would have social and civics systems as identical as their technology - in fact, while the modern technical infrastructure in all cities resembles each other whether it is built in Shanghai or Saint Louis or Stettin, the social, civic and political sensibilities of the people living in them are wildly different. In fact, even political systems like Fascist Dictatorship, when applied to both Italy and Germany, came out very different because the Italian and German Social/Civic systems by the twentieth century were very different in fundamental ways, and political leadership could not change that in a few years.
So, to get the kind of differentiation in Religion and religious policy you guys want to see (and with which I agree completely) I think we need a major revision of the Civic Tree and Social Policy system and the way in which these systems interact with Religion as well as Politics (and the military: many of the differences between the effectiveness of German, Italian, and , for example, Soviet/Russian military in World War Two are traceable to the sociology of their Officer Corps dating back centuries - see Citino's
The German Way of War or Reese's
Red Commanders books)
For starters, Civics are only slightly Linear and 'advanced' Civics do not necessarily require that you 'research' earlier Civics. I'd even go so far as to make Civics 'research' almost completely reliant on Events and 'Bonuses': what is happening to your Civ and what your Civ is doing should be the primary drivers of that Civ's adoption of a given Social Policy or Religious 'Policy' - your job as the Immortal Spirit of the Civ is not to pick and choose the entire Social System of the Civ, but React to the Social Policies adopted. As a result, the further you go into the game the more the little differences will add up to Very Different societies and Civs by the mid to late game. I believe this would be far more interesting and more of a gamer's challenge than indistinguishable, bland civs we wind up with now.
Given that virtually all of the Civilizations in the game actually developed their distinctive Social/Civic features long after the game starts, I think a non-linear Civics Design would be a better option than a 'Starting Civic/Social Policy': given a different starting situation, there's no reason China could not have developed like Greece or Rome, or that Russia could not have developed like Arabia or Sumer or Babylon: the physical situation and events should 'drive' the social/civic development far, far more than it does with the Buffet-style pick and choose system Civ VI gives us now.
That would also mean that by the time you got a chance to 'pick' a religion, the characteristics of that religion would already be different for each Civ: some Religious Policies would be almost Mandated by the individual Civ's Social/Divic situation, while others would be almost Prohibited. Starting from that basic differentiation, the religions should adapt and change like the Social system does, especially as 'your' religion contacts and interacts with other Civics and religions from other Civs. Look at how many religions in the world today have been massively modified by such interactions, or are, in fact, the product of 'merging' two or more earlier religions - and that needs to be modeled in the game in some way...