That's a good point. That's why I would like to see a possibility of converting your religion into Ideology after discovering rationalism in a game. So you can secularise your Civilization. Your religion would be converted into something similar to a legacy bonus from Government Mechanic and on top of that, you would be able to found an Ideology with a new late-game set of modifiers and still spread it with your units and still go for a religious victory.
Entirely agree. Players could choose to convert Faith from Religion to Ideology. It would be good to see 'Ideologies' emerge at ~3 stages throughout the game.
Ancient (or earlier) would be Pantheons, expanded upon, to represent a number of traditional beliefs of your Population or Civilizations Culture.
~Medieval era onwards, players can begin to dispel Pantheons to push organized Religions, which combine Population preference and State preference.
Industrial era or later, Ideologies could emerge, under State control & promoted to the Population, and further aided by the relative removal of Religions and Pantheons.
Pantheon-type beliefs could still be prevalent in the late game, with some benefits for the longevity of the traditions, but with less and less Pressure to modern, Ideology-led Civilizations. By remaining focused on Pantheons or Religions, Reformations are then possible at each stage, in place of upgrading to a new Religion or Ideology.
The conflict between traditional Pantheon beliefs, organized Religious beliefs, and political Ideology beliefs throughout could make for a more interesting and challenging 'Religious' Victory, and make the proportion of followers within a Population matter more. This would also have the advantages of improving the late game, as you rightly point out, and also allow for animist or shamanic (Waashat, Tengriism, etc.) beliefs that either awkwardly fit the current Religious system, or are not included at all. More management of the balance between the advantages and disadvantages of your chosen belief system would be required, and players would have more than one shot at founding a belief system. I've been working on an idea along these lines for a while.