Answer

Bnei, hello.
This topic is very important and very interesting, but it is also very broad and hard to cover fully here. So I’ll address it only in general terms. The halakhic questions need to be examined individually, each on its own.

Let me begin by saying that I have always recoiled from dealing with mixtures and the laws of prohibition and permission, because it is clear to me that I won’t agree with anything there (these are all sorts of ancient physics, or just physical intuitions, that really are not convincing—certainly not today). Perhaps it would have been proper to confront this head-on, but I felt I should leave that for the end.

In addition, I would not define the issue as Jewish law and rationality, but as Jewish law and science. This is not a question of rationality, but of how facts are determined. The question is whether the factual assumptions of Jewish law are determined by scientific tools (current ones) or not. For example, the words of the Hazon Ish are well known (Yoreh De’ah, sec. 5), where he came up with the notion of the “two thousand years of Torah.” It seems to me that he too was rational, except that in his view halakhic facts are not determined scientifically. Several articles have been written about this (Rabbi Dichovsky, Rabbi Rabinovitch, and others. Many refer to Maimonides’ remarks about the laws of tereifot not changing with science, although he too distinguishes between tereifot of animals and of humans. Not to mention the evil eye and demons, which in his scientific view should be eliminated from Jewish law).

And to the matter itself.
1. As a rule, it seems to me that the laws of mixtures assume factual realities and were not intended to be legal fictions (as they increasingly become because of the difficulties), and therefore the very fact that they were established teaches us that, at least in this context, the determining reality is the scientific one. This is how the Sages saw reality itself, not that they simply instituted a scriptural decree.
2. The question is whether old utensils really did absorb and emit as the Sages describe (so that a professional taster would taste them and detect the flavor). If not—this raises the question why the Sages ruled this way. Perhaps we did not correctly understand the meaning of that ruling. For example, the determination that wall thickness is the deciding factor does not necessarily say something factual; rather, they set it as a parameter because they did not know how to determine something more precise in a simple way. If so, then this should not depend on whether the flavor actually exists, but on volume calculations as if the entire wall were full of prohibited substance.
3. A distinction should be made between rulings whose basis is in the Talmud, which has halakhic authority (and even if the reason has lapsed, the enactment does not lapse), and things that were instituted afterward, which have no such authority and can be changed without difficulty.
4. Even within Talmudic rulings, one should distinguish between determinations that were true but reality later changed, and a situation in which it became clear retroactively that the Sages had already erred back then (which in my opinion poses no problem for change, although almost all halakhic decisors do not do this, as with killing lice).
One must also consider whether, when metal today has a different property, this is the same metal as that of the Sages, or perhaps the original ruling never applied to it in the first place (as though it were a new material).
5. Regarding his three arguments for nevertheless retaining these laws, each one has to be discussed on its own merits, and this is not the place for that.
Here I will just say two things:
A. The disconnect he makes between koshering the utensil and the prohibition of the food is puzzling. What is the point of koshering utensils if there is no problem with the kashrut of the cooked food? It is plainly illogical to require koshering as a scriptural decree without any real need. And even if there are medieval authorities who held this way (that too requires discussion), then, with all due respect, their words are rejected on logical grounds.
B. The view among the medieval authorities that nullifying a prohibition ab initio is Torah-level is a lone opinion, and I would not be concerned about it in practice.

I apologize for the brief treatment, but this really is a deep, broad, interesting, and important topic, and I hope that when I have time I will devote a full chapter to it. It is important to address it because this issue makes Jewish law look ridiculous in the public eye.
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Yitzhak:
Is this similar to the prohibition of legumes on Passover, when the reasons change? The road has been repaired…
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Rabbi:
Not necessarily. It may be that it was not correct from the outset, and it may be that it changed. Either way, there is a basic difference: here we are dealing with a law, not a concern or precaution (as with legumes).