How do tight junctions in stratified squamous epithelia affect nutrient supply?
Tight junctions function to occlude the baso-apical flow of small molecules. However, tight junctions do not always completely seal a cell's lateral surface. In addition to regulating diffusion, tight junctions promote cell polarity. Establishment of polarity and prevention of water loss are the major roles of tight junctions in stratified squamous epithelia.

In simple epithelia, transcytosis allows the flow of molecules through a cell with tight junctions. However, stratified squamous cells do not use transcytosis for nutrient supply. 

In the stratum granulosum, skin cells lose their nuclei and become non-viable. In the stratum lucidum, an oily layer is produced by exocytosis. 

It is the loss of nuclei, organells, production of an oily layer at the stratum granulosum and lucidum that contributes most to the death of skin cells, not the limits of nutrient diffusion.