Forgive my ignorance, as I'm new to immunology, however it seems like there would be some amount of positive selective pressure for viruses to develop the ability to continue to present the host's self-antigen on the MHC1 of a newly infected cell, thereby disguising the infection from the body's immune system (or at least from the cytotoxic T cells).
Is this in theory possible? Or is there a reason it cannot occur.
Self antigen is presented throughout viral infections. You seem to think that cytotoxic T lymphocytes respond to absence of self. That’s backward. CTL respond to their specific peptide target no matter how much self antigen there is. In a typical response, there may be 100,000 self peptide/MHC complexes and 100 viral peptide/MHC complexes, and that’s enough for a CTL response.
One trigger for NK cells is absence of self, so perhaps that’s the source of your confusion.
From what I know, the cell does not actively choose to display viral antigens on its MHC 1 receptors. As proteins within the cell are inevitably degraded as a part of garbage disposal, these peptides are transported to the ER, where they bind to MHC 1 and display on the cell surface. When a virus infects a cell, some of its proteins are similarly degraded, either by the cell's own defenses or as a part of their normal life cycle.
So, there will inevitably come a time when a viral antigen will make its way to a cell's surface. The only way to stop it would be to stop protein degradation in the cell entirely, which is not a good idea. What viruses do try is downregulating MHC 1 molecules themselves, so there are less receptors to display antigens, but a reduced MCH 1 expression attracts the attention of NK cells.