ADDED: I also suspect that the average high school student lacks the world knowledge to come up with meaningful guestimates for the inputs to many of those questions.
A lot of the high school mathematics that I learned such as geometric proofs and trig are not all that useful. And it seems as if things that would be more generally useful like probability and stats are not that broadly taught--and are often taught in a very theoretical way when they are.
Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an introduction to "proofs/rigorous thinking", but it seems to me that that purpose could be better served with a first order logic class.
I'm not sure how much I agree.
Sure, the math and the principles involved in designing scientific studies etc. can get pretty complicated. But there are a number of fairly basic ideas that could be usefully taught. And I'd argue that many people don't have a great common sense view of stats and probability. Sure, they have some idea of what batting average means--though there are lots of interesting sabermetric discussions to be had around baseball measurements--but there are also many well-known and consistent biases that many people have. For example, around ideas like streaks.
I've argued before and continue to believe that a semester long intro-level course on stats and probability that didn't get overly wrapped up in a lot of complex equations would be more useful at the high school level than some of the ways that time is used today.
I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.