Balance that is mainly based on economics, not on actual combat performance. It's much cheaper to have peasant on foot then knight on a horse.
Besides there were tons of pikemans as that's easy to use weapon, in LiF you can count them on the fingers of 1 hand even in larger scale battles. Or the medieval foot soldiers were facing cav without battle line, with boar spears, 2h swords and mauls and flanged maces as that's what LiF melees use and don't want to change as that's working just fine for melee only fight.
On the topic of horse archers that's the case only because of the very wrong ingame mechanics encouraging such use. Why does one use horse archers instead of regular foot archers? Because they use the horse as meat shield to hide from enemy arrows showing up only to shoot themself. Then if they see infantry rushing them they just jump on the horse and retreat back to dismount and keep shooting on the advancing melees (the jump back on the horse and repeat). Then lastly in order to relocate to the flanks fast and shoot the enemy from different angles which is perfectly viable in the LiF's scale of fights where 30 vs 30 is big.
This stupid use of horse archers makes the cav to account for such big amount, if that's fixed in some way then you won't have so much cav. Other then that even in LiF it's hard to provide horses for 60 fighters in the guild and keep the supply rolling to sustain combat losses, that's hard to imagine. Yet the majority of the "daily" PvP one can expect is to intercept enemy raiding party (all mounted ofc for the mobility) which means going mounted ofc to catch them and fight them. That's 10-20 vs 10-20 scale of skirmishes, how do you propose doing that on foot or with 5 cav and 15 on foot in the mentioned scale?
The other big thing making the infantry unusable in mass are the archers that break the tower shields in seconds. For example when you see a shield wall of 4 guys with tower shields in tight formation and other melees behind them pushing 5 archers you would expect that to work don't you? Well not in LiF, because in about 20-30 seconds the shields were down (broken) and that group just ran in different direction after the shields were gone and they started getting hit by arrows and were helpless.
PS: When I open the wikipedia as you suggested I see this:
The rising costs of war
In the medieval period, the mounted warrior held sway for an extended time. Typically heavily armoured, well motivated and mounted on powerful, specially bred horses, the mounted knight represented a formidable force, which was used to effect against more lightly armoured troops. Since only the noble classes could afford the expense of knightly warfare, the supremacy of the mounted cavalryman was associated with the hierarchical structure of medieval times, particularly feudalism. As the period progressed, however, the dominance of the cavalry elite began to slowly break down. The Black Death in the 14th century swept through Europe, devastating the population and resulting in serious manpower shortages. This encouraged more economical use of available manpower, and the infantryman was much cheaper to outfit and maintain than the aristocratic knight. The Crusade era also saw a rise in the importance of infantry, and required large numbers of men and material to be organized for distant battlefields. Such expeditions were part of the growing number of sieges, disputes and campaigns throughout the 13th and 14th centuries that greatly increased the cost of warfare for medieval regimes. The relative inexpensiveness of the infantryman, combined with a shortage of manpower, provided incentives for expanding their use
Infantry versus cavalry
Tactically there were only two ways for infantry to beat cavalry in an open field battle: firepower and mass. Firepower could be provided by swarms of missiles. Mass could be provided by a tightly packed phalanx of men. Such tactics were long-established; the Romans used missile troops such as slingers, and the core infantry learned to deal with swarming enemy cavalrymen by forming a hollow square fenced with a solid hedge of iron pila (large javelins). Alexander the Great combined both methods in his clashes with the Asiatic horseman of Persia and India, screening his central infantry phalanx with slingers, archers and javelin-men, before unleashing his cavalry against the enemy. Both mass and firepower could be aided by a good tactical position, such as on a hill or on rough terrain, where enemy cavalry would have trouble maneuvering. These ancient lessons were relearned in the Medieval period; in the Crusades, in the continued operations of forces like the Flemish footman and particularly the Swiss pikeman and the English longbowman.
The infantry revolution and the decline of cavalry
Some Medieval specialists elaborated on the idea of an infantry revolution happening early in the 14th century, when in some relevant battles, like Courtrai (1302), Bannockburn (1314) or Halmyros (1311), heavy cavalry was routed by infantry; however, it can be pointed out that in all those battles infantry was entrenched or positioned in rough terrain unsuited for cavalry, like in other battles of the 14th and 15th century in which cavalry was defeated. In fact infantry had been victorious in earlier times in similar situations, for instance at the battle of Legnano in 1176, but in open ground infantry still had the worst, as shown for instance at the battle of Patay (1429) and the battle of Formigny (1450) in which the vaunted English longbowmen were easily run down; however, the experience of battles like Courtrai and Bannockburn meant that the myth of the invincible knight disappeared, which was in itself important for transforming medieval warfare.
More substance has the case for the "return of Heavy Infantry" as Carey has named it. Pikemen, unlike other infantry, could stand in the open against heavy cavalry. While requiring drill and discipline, individual training requirements were much lower than those for archers or knights, and the switch from heavily armoured knight to footsoldier made possible the expansion in the size of armies from the late 15th century onwards as infantry could be trained more quickly and could be hired in great numbers. But that change was slow.
No mentions of fighting cav with 2h swords, mauls and boar spears
And that's the "melee experience" big part of the players are looking for.