I won't disagree with you about most of that. I will say, however, that people like Archimedes (math and physics) and Aristotle (among other things he investigated embryology in sea urchins) did real experiments and didn't just postulate. The guy who calculated the radius of the earth did a real experiment. The "Antikythera Mechanism" for navigation, although based on a flawed cosmology, was a useful engineered navigation tool that was based on data and testing. Plato to my knowledge did nothing of that sort, preferring to expound assumptions.
William Thompson (Lord Kelvin) was undoubtedly brilliant. But he was notorious for not reading the literature of the day, and often proposed things that others had already thought of. Among his howlers were the following. "X-rays will prove to be a hoax"--not just a mistake but a lie. When a Norwegian scientist did difficult (physically taxing) observations in the snow and cold to correlate the northern lights to solar activity, Kelvin breezily dismissed it (and others disparaged it based on Kelvin's uninformed opinion) because "the sun is too far away". He said in 1901 that "there is nothing new in physics now"--this is before quantum mechanics and relativity, before the structure of the atom was known. In one book I have there is a quote from someone who talked to him about Rutherford's groundbreaking experiments on atomic structure: "I had a long conversation with Lord Kelvin about things of which he hasn't bothered to inform himself". Kelvin calculated the "age of the earth" based on rates of heat escape from deep wells to dismiss Darwin (who based evolution on painstakingly gathered data and still not satisfied only published it when he heard Wallace was going to publish something similar based on his own painstaking field observations), not realizing that radioactivity adds to that heat over time (which he can be forgiven for not knowing about) and that the earth is far from "isotropic and homogeneous" as his calculation assumed (which was known at the time). He dismissed volcanism as "relict heat".
So brilliant or not, I think Kelvin (who also didn't do experiments) was a lot like Plato--a pompous, egotistical ass.