$5000 for a license is about right.
$150k for an ultralight plane is the top end, new. The one Zara is using for her (sponsored) world tour is in that category, but you can get a perfectly good UL plane for a quarter of that price. Fuel is standard car unleaded gas at a rate of ~10L/h, and because UL planes are not certified, maintenance is way cheaper, less palm grease too. Other costs you didn't talk about include insurance, parking, and aerodrome fees, let's say ~$2000/year if you don't timeshare.
So, let's say ok for $50000, but that's not a minimum, that's the comfort zone. The main point of UL is to be affordable. I put it on the same level as driving a nice car, like a BMW or a Tesla. I don't live in the US, I don't know the ultralight regulations there, but I wouldn't be surprised if half of the population could afford flying, assuming they can keep a budget.
As for the lost income, you can fly on week-ends. Many middle-class people have hobbies that take them a significant amount of time, flying is one of them. Of course, just learning how to fly is not getting you a "youngest woman solo" world record, but that's not lost income. As I said, Zara is building something here, it is work, she may even make money, and if she doesn't, we can certainly consider it an investment for her future.
Now, about genetics, it is true that genetics is something intrinsic to all living things and wealth is a construct. But the general idea is that some people are more lucky than others, and we shouldn't dismiss people achievements because it involves some luck, it always does. We could have objections if it only involved luck (ex: winning the lottery), or if it is presented as not involving luck at all (ex: too many "success stories"). But what Zara is doing definitely requires her to do her part and she explicitly acknowledges her luck "I was born into a family of aviators and was lucky to have great role models in my parents and grandparents". So, all good.