This is going to be a classic "computer programmer wants math to be like computers and doesn't get it" kind of take, but In my view the problem of mathematical rigour (or lack thereof) has only become worse over the 20th century and we certainly did not resolve any of the underlying issues in a foundational sense or a practical sense. In a practical sense, it's become much worse and we have many more layers now. In a foundational sense, we succeeded in giving up because we learned that we can in some sense pick and choose whatever is most convenient for our line of research.

That's probably okay if we view mathematics in the way this book (I have not read it, going based on the description here) advocates, as a sort of toy for playing with arguments. And I'm certainly not saying Math should ever be viewed as an empirical discipline nor constrained by that kind of thinking. But I don't think I'm the only one that takes one look at things in the realm of say higher category theory and thinks it's mostly playing word and symbol manipulation games, and lacks any real mathematical content that could not be discovered at a lower and more understandable (and less likely to produce new research) level of abstraction.

I guess I've sort of betrayed that I am pretty firmly a platonist in that respect so make of that what you will.

Like I said, this is not an unusual opinion for a computer person to have and I'm sure it's fairly annoying to any pure mathematician at this point. But I think it's still fair if we want to understand what turns certain people off of pursuing mathematics further.