How do you think of tall games?
This is how I categorize the three playstyles in Civ:
- Tall: 5 cities of 20
+, peaceful Culture victories
- Wide: 6-10 cities of lower pop, peaceful Science victories
- Conquest: 10+ cities of lower pop, Domination victories (or sometimes Science)
All three can go Diplomacy.
- In a tall empire we can support 20 units. I've never needed more than 5 in my tall games (one garrison per city).
- In wide games we have more cities but don't need a much larger army, since we're not conquering anyone.
- With a somewhat small conquest empire of 10 cities and 5 puppets, supply is at 1 garrison in every city plus 25 land military units in our army. I don't think I could fit a size 25 land army on the battlefield...
I haven't ever hit the supply cap myself. The only rare times people encountered it in the past was with 1 capital + barbarians as Bismark, so I altered it for that situation, to make it higher than vanilla.
I'm not sure I recognize what strategy you're using in those screenshots. Is it a conquest game while razing all captured cities? With or without the cap, I'd suggest an occupy+puppet strategy. The only real disadvantage to keeping cities in a conquest game is unhappiness, and we can counter it with:
+2

Colosseums
+3

Theaters
+1

Garrison (Military Caste)
+1

Walls and Castles (Professional Army)
+1

per resource, including surplus copies (Commerce finisher)
A 6

city is happiness-neutral with one of each. Other things like a circus or stoneworks allow us to get higher neutral-cities in the early game, and Police State gives us a big +3

per conquered city in late game.