How many of those combinations do you actually use ? How many have you a strategic need for ?
I have nothing against the notion of a game with a thousand different units, myself.
OK, here's a thought that combines a couple of notions I've seen in different mods (The Balancer and Rise and Rule) with a couple of other notions to put together a model for how lots of units might work late-game.
Posit quantitative resources.
Posit units that need different resources to build and use them up to different degrees.
What there could then be is one tech track of units that need one set of resources (for example, iron, rubber and oil.) If you have iron, rubber, and oil enough you can build tank-track units with it, and as you learn the appropriate techs you upgrade your tank-type units through a couple of generations of tank technology.
If you only have two of those resources, you can only build a different track of units - say, armoured cars. But you have good strategic reasons to build armoured cars even if you have the capacity to build tanks - maybe they're a lot cheaper and useful to bring with your tanks for cleaning up the leftover injured or weaker defenders in an enemy city. Maybe you need a different track again to build units with decent anti-aircraft defences in order not to have your force of tanks and armoured cars wiped off the face of the map by bombers. Maybe you want
another different track to build units best suited for defending cities once you take them.
(It seems to me that most of the useful things promotions actually do are basically compensating for the way units in Civ 4 have only a single "strength" value; they are effectively allowing you to pump up "defence" specialist units with Combat and Ambush and "attack" units with Raider, Barrage and maybe Drill, no ? Which units where attack and defence values varied separately would not need to have.)
What that would give you would be a strategic landscape that varied depending on what resources you had available, what balance of forces you need, and on which resources you could take from your enemy when.
The other notion I like, which is in Rise and Rule in the earlier game, is stepped unit promotions. So you can build heavy horsemen; then a bit later you get the tech to build cataphracts, which are a slightly better cavalry-type unit; then slightly later again you get knights, and heavy horsemen upgrade to knights but cataphracts don't; and later again you get curiassiers, which cataphracts upgrade to, but knights don't. (I think I have all the steps along that path remembered in the right order; I may not, but it's the general concept rather than the details I am trying to convey here.) This is an interesting mechanism for the balance it requires you to judge between building new units and upgrading existing ones, which stnadard stepwise upgrade paths do not do.