"My" ideas 3/3
Civ: Assyria (this is basically gonna be an updated version of civ 5's but rebalanced for civ 6). Ability: Treasures of Nineveh. When you conquer a city, any great works count as "captured". Captured great works now produce an additional +1 yield depending on their type (science for writing and artifacts, faith for relics and religious art, production for sculpture, gold for music, culture for landscapes and portraits, did I forget any?) and an addition 2 tourism. If you raze the city, great works are transferred to your closest available great work slot, if you have a compatible one (if not, too bad!).
Leader: Ashurbanipal. Ability: Cultured brute. When razing a city, Unlocks the "library of Ashurbanipal" unique building, which replaces the Palace. When capturing a city if you raze it, or instantly repair all pillaged tiles (not districts + buildings) instantly if you don't.
UU: Sapper. Replaces Battering Ram. In addition to the regular siege tower benefits, units stacked with or adjacent to it get a 50% defense boost from ranged attacks and can pillage for 1 movement cost. Works against ancient + medieval walls, not just ancient ones like battering rams. Can construct one Ashur statue in neutral or enemy cities.
UI: Ashur statue. Can go on any tile, built by the sapper. One per city, and can only be built in neutral or enemy cities, plus one in your capital (which can be built by a builder with Masonry). +2 faith and +2 culture (culture added to tourism after flight). Goes on any terrain. Your units within 3 tiles of an Ashur statue gain +5 strength if in enemy territory. Every time you capture a city, every Ashur statue in the world gains +1 culture and faith, and an additional +1 each if you raze the city. Cities with an Ashur statue have +1 loyalty.
LUB: Library of Ashurbanipal. Replaces Palace. In addition to what the palace usually does, has 1 art slot, 1 relic slot, 1 writing slot, 1 music slot, and one "anything" slot like the regular palace. When at least one of these is filled, units spawn with a free promotion. If all five are filled, get a theming bonus. Works placed in these slots give the "conquered works" yield bonuses regardless of if they were actually conquered. Once you build your first theater square, the Library of Ashurbanipal also gives 1 artist, writer, and musician point per turn.
Comments: Conquering happens a lot more in Civ 6 than 5 IMO, so a free tech for each one would be overpowered. More focused on domination + culture as opposed to civ 5's domination + science. Ashur's building being a palace, which you get for free on turn 0, may be a bit too OP, which is why I didn't give him very much other powers, although to be fair the replacement won't do anything different immediately. You'll want to keep some Sappers around and mix them with Siege Towers.