I 'd like to add there is no such thing a cheesy army in a blind challenge, at least IMHO. Swiss can be beat ( free company vs swiss is a really fun line up) Spartans are fun on paper but I honestly think that a regular hoplite army is better balanced and fairs better ( then again I never do to well with offensive spear armies) Hardened cavalry can beat horde armies(at least in open)
light foot can be a pain but only a few armies are unbalanced by them ( basically the LAtin greek lists, which is a shame as I find the history of post crusade Greece fascinating...)
Simply reducing their moment to three hexes vs 4, disallowing them from sacking camps AND not allowing them to "hold firm" in open terrain vs anything other than other lights would go a long way to making them more historical, and curb their use to entrap other troop types and most commonly JACK the BP of your army for cheap, uncatchable troops..
The silliness in terms of unbalance of horde armies , fortunately, is confined to only a few lists. The host of Scotts, Scotts islanders, Irish, Anglo Irish blah blah blah as well as the Nubian Christians are the main offenders. Ironically these "armies" historically would have been tiny , more likely raiders vs a formed army.
One thing that can help in understanding the overall effectivness of an army is the efficiency of its troops. If the army can access enough of a high efficient troop type, it can do very well indeed
IMHO the three most efficient(cost vs power) troop types:
medium protected impact foot
superior protected lancers
poor light bows
(medium unprotected superior archers also take the cake but they are only present in the Nubian lists so ...)
There are variations though that break this "rule". In the later lists with a significant drop in the quality of infantry in general, army lists that have any impact foot tend to be a pain to deal with. So list that feature dailami or almogovhars have an edge (more impact foot)
Altogether the game can be very satisfying and I believe that you can have reasonable tactics that are broadly similar to what would have been used without having to specifically find opponents that want to play in a certain style, or limit army compositions. The true culprits though are huge armies where a player simply lines up an army from left to right, stretched across the board. Considering rear hit are one of the key components of the game, the smaller army will be flanked on numerous fronts across the board and will have a tough time.
The problem would be command and control but FOG does not have that, so really the only way to mitigate this would be the maps themselves. More limits in deploying near the flank edges, allowing deeper maps so its easier to deploy in depth. Would players min-max a 80 BP designed army of light spear infantry IF they were forced to deploy them 4-6 deep?

Probably not and likely one would see better balanced armies in those situations.
Cheers!