As far as generals go, I don't usually use Cavalry Archers (CA) as generals. It's true that they are very mobile and can usually avoid trouble, but I prefer my generals to have speed and high morale
Ditto, for me. In addition, my cav are usually out on some flanking mission or even behind enemy units, and therefore not always in direct contact with my main force. If I slip up and they get caught/routed/destroyed, well.....there's usually more where they came from. But if they're an heir

I have no qualms about having SA heirs. My archers are usually tucked safely behind other units. What to do with them if they run out of arrows can be problematical, however...................

I've even experimented with musketeers as heirs. Never considered it before I got me a 4-star teppo general in a campaign once........added a bunch of BFN and a couple of Kensei and he became my 'river-buster'. Had a lot of fun with that one.....he even made 5-star..