Are self-recognizing Thymus lymphocytes more central than people consider?

Antigen presentation to T-cells with MHC I and II is a young science. It has not been explored that long. Younger than antibodies, since those were observable more easy. And since antibodies clearly bind to non-self, there would be a priori prejudice to assume T-cell receptors did as well. It is known that self-antigen are fewer than non-self. This is self-evident. What is not as intuitive is that the self-antigen that MHC can present, is only a fraction of all self-antigen peptide fragments that can be produced from the human body. And T-cells that learn to recognize self, with one self-antigen per T-cell receptor, would only have to recognize the self-antigen that MHC can present.