I have no cavalry yet, only basic yari and archer units, and I have been able to have large armies because I fill up with cheap yari ashigaru. I have had some success with using them in flanking and as shock troops.

I also use ashi as garrison in newly conquered provinces and position my main force for the next attack. The ashigaru units actually become useful with some experience; a 2-3 honour unit don't scare when someone cough nearby, but the fresh units will run if you just look at them, hehe.