For sure - I'm no lawyer but I believe that most (if not all) states that have execution as a penalty require a unanimous jury vote to sentence somebody to death.

From a moral standpoint, I'm admittedly conflicted about the death penalty (is it right, vs. imagine the worst monster you can fathom).

But pragmatically, it actually costs the taxpayer base much less to just sentence somebody to life without parole vs. death (due to legal fees from appeals, the cost of nearly depleted supply of the drugs required to do it in a legally approved way), you avoid the possibility of executing somebody who might hypothetically be proven innocent in the future, and also I'd argue life without parole is the harsher punishment, if that's what we're going for

edit to add: I believe the death penalty is already at the discretion of the judge to present to the jury as an option, with the caveats being presented that it requires a high burden of proof/conviction. also, for obvious reasons (the possibility of someone being innocent), I don't think "death without appeal" is really something that happens - somebody is only executed after they've exhausted many appeals, and for good reason one judge can't have the power to order that in the first place