It might put away the fun of having "alternate History" and researching nuclear weapons in 1600. Personnally, I don't take attention to the year, much more to the number of turns. Maybe something should be done for us to take more attention to the date. It would be more immersive, but I have no clue of how to do it simply by creating special events with the date that the main focus would be to remind the date. (maybe Rankings to different part of the game as we had in Civ5 ?) The date would be highlighted or something.
As to me, your idea recalls me of one of my ideas to play the date rather than the turns. I mean, I think it was something like XCOM 2 when you are doing something that takes time. You are pushing the button "start" (here : end of turn) and the years scroll within the AI turn, possibly prompting you in the middle of it when something you began just finished. Everything would be counted in years, and turns would have variable number of years within them like it is now. Thing is, things to do would now count in years, not turns, which would be a lot more realistic and less "a wall (race) into the end", I mean if you have 500 turns there's nothing very exciting that can happen, because it has to be a linear development. If you introduce years (or months or days, as far as I know, maybe just as fractions of years), you suddenly have more space (time) to fall, rebuild, change, etc. That would be a massively useful tool to at last, make us feel the rise & fall of civilizations. I'm just not sure how it would work in multiplayer. (I guess it doesn't HAVE TO work, you simply run the game turn by turn as in the old Civs ? After all multiplayer has to be competitive, and that's not a big deal if there's an "end wall", it is to say things being more linear and a competition (sometimes unfair, but always challenging) of doing things better than your opponents. So, I guess multiplayer could remain the old way in every aspect. Give the ability to the player to play alike in single player too. Maybe that for old players the first game or the tutorial would ask how the player wants to play, and how to change it. (new players wouldn't understand the difference, so stay vague about it) The option should be quite accessible, like in the advanced game setup.)