The way I see it, being mounted is a trade-off. He doesn't need to traverse peaks. Let's assume a Brigand gets a split promotion choice of Berserker or whatever someone calls the Mounted class:
Berserker: 6 move, crit bonus, can walk on water and peaks
Mounted: 8 move, access to bows, different caps.
You're trading out the berserker bonuses for the extra move and weapon versatility. Now obviously anyone using it is free to alter stats as they see fit. Walking on water or peaks is very situational depending on the map but you can use 8 move on any map you want. It comes down to what you want on your team. Since Berserker can be promoted into from Pirate, maybe you want to go for the mounted axe/bow user unique to Brigand instead?