From what we know about the Dothraki. Misogynistic, superstitious, fearful of witches I agree that Dany's plan shouldn't work. Based on their own rules, the death of the Khals and all their blood riders would just immediately create a power vacuum that any strong Dothraki could fill in the same way that a new Khalassar was created almost immediately following Drogo's death. Sure she survived the fire but what's to stop anyone from just walking up to her and stabbing her in the face. Even Drogo had to prove his strength within his own Khalassar in order to keep respect. Dany wouldn't be able to do that but based on Dothraki culture a physical challenge to her rule should be expected. Mirri Maz was known to be a witch as well but that didn't put enough fear into the Dothraki to save her from rape or enslavement.
There's a lot of reasons why it shouldn't work. It would have been better if Drogon had torched them. Even better if she was mounted on Drogon while he did it. I feel like the Dothraki would more easily fall in line for a dragon rider/tamer.
I wonder how far from the book they're going if at all. I'm still expecting Dany to visit Asshai because of Quaithe's warning. She was right about everything else.
As far as I can tell, the Dothraki seem to be functioning through a strict hierarchy when it comes to the ruling class. They have the Khal, the Khaleesi and their Blood riders with the remaining set being just soldiers. So if someone had challenged the Khal and killed them off, perhaps the Blood riders avenge or they switch allegiance. In the case shown however, both the Khals and their blood riders seem to have been killed. This creates a 2 tier power vacuum which causes the immediate reaction of bowing to the power which made that happen. Yes someone from the tribe could have taken the initiative and tried to attack Daenrys but that's not how a social hierarchy works unless the lowest segment of the society is terribly pressurized to commit actions against the rules set by the group they live in. The lower rungs in rural social hierarchies generally have higher amounts of servility and lesser thought of questioning the hierarchy itself.
We also know that the Dothraki are superstitious so any exuberant show of "magic" which ended up killing their Khals is definitely something that would make them bow down to it. Add to that that she is an ex-Khaleesi and one of them, it would in fact make them respect her more than a random witch