Is this not what Descartes tried to demonstrate with Cogito ergo sum? Similar to your second point: "it is self-contradictory to say that we cannot think something about something", Descartes argued:
[W]e cannot doubt of our existence while we doubt
Later, Charles Sanders Peirce's pragmatic criticism of Descartes does not remove principles, but instead enshrines them:
We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. … A person may, it is true, in the course of his studies, find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it, and not on account of the Cartesian maxim. Let us not pretend to doubt in philosophy what we do not doubt in our hearts.
In a sense, you could say that Peirce is arguing for more principles, and that as we go about our studies, if we have to undo some of our principles along the way, so be it. Peirce's principles then wouldn't be "true" principles, but "working" principles.
So, if anything has happened to the discourse of principles along the way, it is that we have decided that two extremes -- 1) We can conclusively determine self-evident principles and 2) We cannot assume any principles -- are not useful. We can assume certain principles for the sake of a foundation, and then later on if we need to revise or reject a principle, we can revisit it at that time.
Reference: Cogito ergo sum - Wikipedia