Allow me to state my natural instinct to this title;
noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo. No, no no.
It fits them as much as the throwing daggers+ Swadians idiocy. If you're having trouble fighting Nords and Swadians in Melee as Khergit, maybe do as the Khergit do? NOT GET INTO ****ING MELEE WITH THE DOPES.

Maybe your arrows don't do enough damage, that'd be a better suggestion. Maybe there are other, unfair to you, (dis)advantages to Khergit meleeing, but an infantry class? Is that honestly necessary?

If you suck at handling one situation, try different tactics? Work together better. Have the enemy point their shields one way and then have someone else attack from an unprotected side?

Enemy too heavily armored, keeps killing you? Buy a mace instead of a saber? Maybe a pickaxe if possible.
Anyway, those are my reasons not to have Khergits have infantry.