Ait primo: skirms for the inca player aren’t exactly too useful in this situation.
In post imp you are unlikely to be able to micro individual units(not that it’d make any sense to do so) so in our mongols vs inca scenario skirmishers would automatically path into attacking hussars(since they are also too fragile).
Secundo, mongol hussars are extremely strong; and they are able to almost take out a fully upgraded incan eagle in a 1v1 fight, while being far, far more cost effective.
Tertio, there’s no such thing as “catching CA”. To take out an army of mangudai you’d need a comparable number of eagle warriors with no terrain penalties, nor chokes, and even then the mangudai are going to be able to take a reasonable-ish fight. But against a competent player that’s just never going to happen, because mangudai+ hussars are always, always a much faster army than eagle+skirm+halb, the mongol player when he sees that he is losing will just pull back to a castle or other defensive position and wait for his hussar numbers to replenish.
Quarto, in the end it comes to meelee pathing vs stationary ranged units. DE has very significantly decreased meele units’ ability to choose reasonable paths when approaching other units. A battle of mangudai vs eagles won’t come down to states, but the fact that in most cases you’ll have at best 20% of your eagle numbers actually engaged, whilst for mangudai it’s always going to be 100%.
Think about it: if it takes, say, 5-10 seconds for pathfiding to find a way for eagles to take a reasonable fight, and before that they just keep getting stuck and don’t really contribute, as mongols you can reset these 5-10 seconds by just retreating 5 steps, which is always going to be enough for the eagles to start struggling again.
And no, there’s no actual “proof”. Most games at competitive level between these civs is nearly always going to end before the post imp stage.