True, if the MC would have been a real threat to her or the stability of the empire i would agree with her order to kill him.
The thing is, she has spys there, MC was never considered to be the next boss there, he has shown zero ambition to take over that position and neither does he seems to have any goal to start a rebellion against the empire.
MC is just an elite soldier, that's it.
Dante is the only son and official successor, it be strange if she didn't have an eye on him.
Also he has no achievements and is much more likely to do stupid things to prove he deservs the possition and is a good ruler.
That's pretty much the kind of arbitrariness and tyranny which either gets a ruler assassinated or starts a rebellion (i assume the MC wasn't the only case of her great judgment).
Dante, gullible as he is, has listened to the first guy which showed up, was promissing him some things and is trying to overthrow the empire...