We do indeed, live in interesting (or depending on your worldview, dangerous) times.
This article also made me think of Rand, and I wish they had some awareness of Rand's epistemology. They do mention Bayesianism, which is a useful framework, but still has limitations. (Recently I've been reading through classic papers on probability theory (Bayes, Bernoulli, E. T Jaynes) to see if it can be combined with Rand's neo-Aristotelian view of concepts).
Regarding my comment on the article, it was really just an "excited utterance" when I realized that the "shut up and calculate" and "bury the contradictions" tactics in Physics had run its course. I really wasn't looking to engage and offer Rand as the alternative to Kant. Physicists really want answers and seem more open to questioning their basic premises, including the premise that Philosophy is worthless. I feel like there is "revolution in the air" so to speak.
I too like the Bayesian approach to probability especially the work of E.T. Jaynes. I bought his book and though I didn't fully understand it, I like the idea of probability as a generalized logic of science. In his framework the problem of induction becomes when is it valid to conclude a probability is equal to 1.0 not 0.999.... This is the key because the latter is what leaves the door open to the skeptics.
(I previously tried to PM you but the email bounced, I will try again).
Sounds like you've been reading too much Ayn Rand. Nobody else places as much irrational blame on a single philosopher. Even if you think his philosophy is wrong, its much less wrong than things that came before it, and is certainly less wrong than claiming you can found a philosophy on 'A is A'.
A separate link leads from Kant to Frege, Russell and modern analytic philosophy. Which is hardly on the level of Marxism, and it still respects reason and reality, but it led to the idea of logic as meaningless symbol games, rather than a vital tool to understand the world.
Rand didn't found her whole philosophy on 'A is A' - this is a common misconception. She isn't trying to create a philosophy based on geometry, where everything is deduced from a few axioms. The law of identity is fundamental, but it's not sufficient - you need observation of reality too.
I don't see why this has to follow.
Oversimplifying out of necessity, there's been a long running philosophical conflict between empiricists (focus on reality) and rationalists (focus on theory). The hard sciences have managed to avoid the problems of philosophy for the last few centuries, but are increasingly running into fundamental methodological limitations. If, following Hume, induction is unreliable, how can we ever know our scientific theories are valid?
Ayn Rand developed a novel epistemology and theory of concepts to deal with these issues, but she's almost universally slammed in academia for her political views.
All I can suggest is to read both her and her critics and make up your own mind. (But do read her own words, not just what her critics say about her - the book I mentioned above is a good starting point).