Why do they want it? Can't they self-fund it? Or do they just want other people to share the glory? Isn't the equipment shown in the video worth as much, or probably more?
"They certainly enjoy funds orders of magnitude more."
Certainly? If they had the money already they wouldn't be asking for it. Perhaps they have had this proposal declined once or twice by the agencies. Science is very competitive and the majority of proposals are not successful: 10% acceptance rates are not unusual. It's also highly winner-take-all since winning funding tends to generate output which tends to attract more funding.
"$50K is like two YC startups' seed money."
Which is loaned in expectation of a return. Science funding is a gift in the hope of a long term strategic advantage. The government doesn't just hand out $50K to Prof. Doe on request. Besides, $50K would barely support one PhD student-year with 50% overhead and tuition.
Researcher profs spend a large proportion of their time on grant writing and only the best are successful, and while it does come in large chunks when it comes (in the US), the expected value of each application is not high. It's much easier for the currently in-vogue fields than others. It's also hugely easier if you have a little industrial funding, as there are many matching programs. This means getting the attention of the industrial players, if there are any in your field. Very time consuming!
I suppose I get it, but I thought Kickstarter campaigns required a deliverable end result as a result of contributions?
As best I can tell, the direct impact of the kickstarter funds will be paying for a camera to put on a launch vehicle to watch the CAT engine, but it's not very clear.