Why is thymidine incorporation (DPM) normalized to per mg protein content while testing for cell proliferation?
I'm not sure that there is a strongly disciplined reason for the mg protein content as the normalization, but there is obviously a need for some normalization for different amounts of tissue- if you use 10X as much tissue, you should expect DPM to be 10X as high!
For example, in this somewhat old paper, They normalize not to protein content but to wet tissue mass or to intestinal crypt count (as they are looking at incorporation in intestinal crypts). So the normalization that you observe is not universal (or more likely, is a more recent innovation). They observe that the cruder measure of wet mass provides a poor normalization:

Instead there was a positive intercept of dpm/mg tissue which represented about
25-30% of the maximal tritium content of the intestine. (abstract)

That is a good reason to use a more precise normalization! They find that the more precise normalization of dpm/crypt works better, presumably because the crypt is the incorporating tissue.
I would suspect that the dpm/mg protein is simply a more precise method for normalization.
A yet more precise method would be the one used in this 1987 paper, in which thymidine incorporation is estimated as dpm / microgram DNA- here, you are actually directly comparing to the mass of the DNA, which is where thymidine is incorporated. That is a more obvious normalization than protein content.
However, for crude tissue extracts I suspect that it is more straightforward to estimate protein content than DNA content. So protein content is used as a &quot;good enough&quot; normalization.