You're probably doing something wrong then. Or maybe you're playing on VH battle difficulty where militia>guard infantry. Lancers being killed by militia in that manner is unheard of in my game (M battle, VH campaign).
If you're using carbine-armed cav to only chase down routers, you're not using them properly. They should be place behind your line infantry to create, along with light infantry in front of the line, 3 overlapping fields of fire. Chasing down routers should be secondary; in fact, heavy cavalry is better at chasing routers because they take almost no casualties while doing so.
I use 2 heavy cavalry and 2 light dragoons in my stack. The light dragoons form my third line that can fire without causing friendly casualties. The heavy cav protects my flanks from enemy cav, protects my artillery, attacks enemy artillery and specialist troops (grenadiers/light infantry).
There is only 1 type of unit you should be afraid of, and that is square-forming infantry (probably elephants too but you don't see too much of those). The fact that its still possible in the game to form square AFTER you've been charged makes any type of cav completely ineffectual against. Maybe they'll change that down the line more.
RTW ruined cav expectations for this game lol.
@Servius
You can recruit Uhlans in German/Austrian/Polish regions.
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