Ok guys, melee units used to have city raider promotions. It was one of things carried over from civ 4.
It got removed because it made cities too easy to conquer. Declare war and have a bunch of rapid melee units with city raiders charge across the border and slam into those frontier cities and take them down fast.
If you install vanilla civ 5 unpatched, i think the promo is still there. And there is 3 ranks of city raiders. 1/2/3. a melee unit with rank 3 city raider could just knock like 75% of the city's hp off with one hit or oneshot it if there's a disparity in tech advantage.
And panzers used to be able to conquer cities with just one panzer.
How you say?
Well make sure that panzer have blitz promo then have it park next to city and wait for next turn so it can have all six or 8 movements it can use and attack city repeatedly until the city run out of hp. I took massive amount of cities with blitz/cityraider promoted panzers.
I could just dow on five AIs at once and send out all my panzers and crush them all at same time. I have done this at least once
panzers with city raiders/blitz promo = broken and cities cry when they see them show up. That was in vanilla civ 5 xD