I think there are a lot of good ideas here, but I tend to agree that the types make me choose what to build and where. Now, that does limit future choices of what to do with a particular starbase once built. But I'm pretty much okay with that.
I'm not trying to derail the OP, but in my opinion, I'd prefer an alternative to or variation of universal design...
If I had my druthers, I'd like to see a system that makes it possible to diversify but more cost-effective to specialize. For example, A base that is already mining can more easily be made into a better mining base, but economic modules could be added--either at higher cost, at some disadvantage, or both. This way, depending on the tech you've researched and the resources you have, there would be a choice--do I take that economic bonus I desperately need even though it has significantly more upfront cost, or do I add that mining bonus to get more of the resource I am always running out of. (As the game is now, this wouldn't result in any real choice, though, because by midgame I am generally swimming in resources and cash.)
I would love to see something like that coupled with the ability to have combination-based choices. If you have a certain economic module and cultural module, you unlock a special module. However, that module isn't available if you have a certain military module (or maybe if you have too many military modules installed, and then you can't add more once the improvement is built).
Maybe some or all of these special modules could even be one-per-civ. Of course, I suspect this could be very difficult to implement, probably most of all from a UI perspective (and maybe not), but I think creating choices like this would make starbases incredibly interesting. Each starbase would have the potential to be a unique contributor to your empire, develop character (much like planets do), and become truly valuable and strategically important.
But for now, I'd prefer to keep types and require me to choose where my administrator ends up. As the resource system and game in general is refined, I hope starbases can become a bit more interesting and offer more opportunities for meaningful (strategic) decision making. (And that isn't really a criticism of the current starbase system, which I like a lot--and relative to the base game, I mean a lot a lot.)