I'm playing my first ever Takeda campaign on hard, and so I'm doing my best to make good use of our elite cavalry. My first army had a solid 5 units of light cav. Once they got some experience, they actually do very well! You just need to seriously keep an eye on them, because they will absolutely melt if the wrong unit catches them in melee.
I don't bother too heavily with any overly complex formations. In general, if I'm defending, yari-garu form a defensive wall, katana samurai positioned intermittently along the line in small gaps, (so they can burst through once the enemy gets stuck on the yari wall), and yari samurai on the flanks, preferably hidden in woods. Rapid advance makes these guys fantastic flankers, and also perfect for catching enemy cavalry or lone units which try to run around and catch your archers. Yumi-garu form up a nice staggered line behind the wall, and just shoot things all day.
Cavalry go on each side and at the start of the battle, they begin walking the long route to get behind the enemy. Sometimes you draw a few enemy units away to chase you, (which is fine), so you just avoid them, or if they get separated, charge them! If a single bow unit gets out of position to try to shoot your flanking cav, you can usually charge, kill half the unit, and bail before reinforcements catch you. My cav then just sort of walk around behind the enemy until the lines clash, and then charge various points in the rear, or just take out all the enemy archers before joining the melee. If the enemy sends a significant force of yari-armed troops to chase my cav, then I never really engage in melee, and just have a long goose chase. The enemy's main force will be weaker and they'll usually lose the main engagement pretty handily.
If I'm attacking, the yarigaru form a wall as usual, advance together, and samurai units generally flank. Cavalry will take a much more aggressive stance, and run full tilt behind the enemy lines early. You lose some stamina, but you often break up the enemy formation. Some units break off to chase you, or their archers reposition themselves to shoot you, and you just stay out of range but behind their rear or flanks to threaten charges until your main line hits. Once the melee starts, you can focus 2-3 units on any one spot and they're almost guaranteed to break instantly.
My campaign is still new, and so I only got yari-cav a few turns ago, and only just incorporated them into my force. They're certainly stronger, but they feel so much less expendable. When I lose light cav, i don't really care much. They're as cheap as ashigaru units! When I lose yari-cav, I feel sad.
So overall I'm loving lots of a cavalry. Just takes a lot of micromanaging because again, if a unit gets caught by like yari samurai or something, they'll all die in seconds. To make matters worse, my enemies AND allies are building armies composed of like 75% yari samurai. It's kinda crazy! Do they always do this? I just wiped Hojo out and the stack defending their capital was literally 15 units of yari samurai, their generals, and 1 unit of yumigaru. So rude.