Using dragon usually involve burning things to the ground and if we want the prestige of winning a war we must be involved in a war.
I will point out that if Rhaenyra is trying to separate herself form Daemons way of doing things asking people to die for your glory isn't a good way to do it. Daemon would be all over that idea like white on rice. I also don't see Rhaenyra as the type that would truly enjoy war in itself she'd be similar to Rhaenys in that I think. Fight when necessary but don't go looking for trouble, very similar to the fist fight she got into as a kid.