She is recruiting random little folk to tame dragons. She doesn’t know these little folk. They could easily just take the dragon and do whatever they want, be it join the greens or fly away with it and just chill for a bit. There’s not really keeping them loyal to Rhaneyra.
Another issue is that she’s assuming the little folk that tame a dragon are willing to go to war. Not everyone is willing to face that level of danger. They may say they are and even mean it, but when the confrontation is about to happen and they realize the danger they’re in, they could easily renege.
Lastly, these people could be mad. They could potentially just burn a few important people when it’s least expected.
The whole strategy seems deeply flawed.
Put yourself in Rhaenyra’s shoes: All she knows is Daemon has fucked off to god knows where and she cannot win the war without more dragons. You make good points, though. It’s a hail mary for sure.