First, why is a chief medical doctor involved in the development of some kind of energy shield for spaceships? This would be Jordi's topic. It jus has nothing to do with her field of study and science.
Second, why would such a major invention be tested a) with real test pilots that just volunteered and b) with just a handful of people? As always wirh Star Trek, press and media seems to no longer exist. If on earth someone tries to swim over the channel, tries to fly around the world with an EV plane or other stuff, hundreds of people are present and it is covered by the media. Here we have something similar as a rocket launch or a free fall jump from space and there is NO ONE around??? Here Star Trek always massively failed. There are also peace treaties signed by whole planets on the Enterprise, facilitated by Picard and just a handful of people are present when history is written that will affect the live of billions. On earth hundreds of diplomats, envoys and other people are involved even when two countries just sign a trade treaty!
And as always: You can disobey order on the Enterprise. As long as it turns out, that you were right in the end, you have nothing to worry about and can just keep your rank, position and assignment. You don't even have to face civil charges made against you by the family of the dead Ferengi. So not only media and press is non existent anymore but also lawyers and civil courts. And if course police. We don't have them. Murder investigations are conducted by ship doctors. No police whatsoever investigates, interviews the suspects. It is ridiculous.