Just as a disclaimer, I have not played Civ 7 myself yet, but I find this design choice interesting. These are just my general thoughts about this kind of mechanism. Please correct me if I have misunderstood something.
One of my main issues with Civ 6, is that the outcome of the game was decided long, long before the actual end of the game, and so the endgame became incredibly tedius to me. I think this is to some degree unavoidable in any game which involves snowballing, and since snowballing is often fun, I'm not saying it should be avoided at any cost. However, I feel it impacts different games differently. I know not everyone agrees with me, but I found it a lot more egregious in Civ 6 than in 5. In Civ 5, you didn't have nearly as much to manage in the late game, things could be automated to a higher degree, and you would also get new things to focus on, in the form of ideologies and cooperative projects. In Civ 6, I feel I was doing the same things in the late game as in the early game, just a lot more of them, for less reward and impact, as the outcome of the game was decided many hours ago.
It looks to me like the age system in Civ 7 is a means to combat this, by changing things up a bit between ages, and introducing more distinct gameplay for each age. The idea is not unique to Civ 7 - Ara: History Untold does something similar by culling the least prestigious nations between acts, opening up their resources and lands for expansion by nearby nations. Civ 7's approach seems a bit more involved, or if you don't like it, heavy handed. For my own part, I have to reserve judgement until I actually play it myself, but I'm not against it in principle. What I have seen of it, I honestly think it looks promising, with some meaningful choices, and points being assigned to "level up" your leader and civ. I'm sure there's a lot of room for tuning and refining the mechanism, but I suspect that this is something I am going to like.