This is a common problem with 4X strategy games. In the beginning, you make fewer, but more important decisions. At the end, you are making many more, but far less important decisions. I think it was a bit better in Civ 5, for a couple of reasons:
- I could play tall, which meant I didn't have to spend 90% of my time making mundane decisions about production queues. These are interesting in the beginning, when you just have a few cities and every decision matters, but a chore at the end. I actually prefer clicking "End turn" over and over to doing chores.
- There were some new elements introduced in the late game, mostly related to the World Congress, ideology and cooperative projects.
There are different ways of dealing with this, but in general, I feel the best approach is to minimize the micro-management, and introduce something new to do instead. Reducing the micro-management can be done by making tall viable, or by at least introducing some limitation to how many cities you can effectively manage directly in some way. This should be done anyway, in my opinion. Another way would be to enable some degree of automation (production queues, governors), or add UI features to manage larger empires. Improving performance and turn times would also improve the experience.
As for adding new things to do in the late game, it's not hard to come up with ideas. Expanded diplomacy, expanded espionage, world congress/UN/planetary council, end game crisis, cooperative projects, lunar/orbital expansion, information warfare, economic warfare, there are many possibilities. It would be especially good if these new elements could potentially change the standings of each civ, without making what happened earlier irrelevant. It is not impossible to achieve that. Elements like spies are not necessarily tied to the other strengths of the empires. The way ideology worked in Civ 5, you could have a bunch of other players choose a different ideology, influencing your people, and soon your empire was unhappy. The blooming of the planet in SMAC changed the map, and could disadvantage more technologically advanced factions. Just to mention some examples.