surely I should get to choose what happens to at least some degree.
You do. You can pick from the cards. If they don’t line up optimally then you pick your best option and go with it and yes sometimes that is just one card even after you mulligan.
TBH I rather like the combat system. It is a bit random at first, and you probably should never fight anything before you get the symbiote (and throw out the stamina recovery card). But when you get more sigils—and especially after dropping ranks in Valiant Rush—it comes into its own as an interesting exercise of making the best use of the hand you’re dealt.
If I were to make a change to it to make it less random, maybe it would just be to add some power that lets you mulligan more often, or that lets you do a 4>1 or 1>4 chain sometimes.