I am personally split in this debate that men on horse back should have faster movement.
Over short distances, yes they are more mobile, especially later in the game's time frame. But at the same time, setting and breaking camp takes longer, as there's simply more to do.
It would be nice to have "Range" added to CAVs movement. Two speeds if you will. A CAV army could go maybe two provinces at high speed, but no more. And they would have to rest afterwards, so they would recover moral slower.
This would enable that 'rescue' you need every so often, or that blitz attack... But only if you prepared for it ahead of time, and only within a limited range.
Another concept that has finally been crystallized is that the speed of CAV is on the battlefield, and is well represented with flanking and shock. I feel the move makes you deal with "the army" as a whole, not "the INF Army" and "the CAV army", and never the twain shall meet.
Us modern humans are spoiled by hopping in the auto and driving across town and country in minutes and hours. Given the wagons and paraphernalia that accompanied CAV units that carried the important essentials... like food ...didn't, can't, and won't travel at the speed of the Cavalry rider. Even when traveling the 'roads' of the day, the loads couldn't be pulled at full gallop all the way across the country.
In many cases, it's a simple case of no longer having or being able to process the concept that a 20 mile drive could take all day.
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