i see exactly what you are saying. shoulder protraction. but in that position, shoulder protraction is done by anterior delts, and pec major and minor, the lats are involved only slightly, but not to the degree you say, only for internal rotation, not in the actual press. rolling your shoulder forward is the degree of involvement, at which point, your shoulder should be retracted and fixed in place soooo......
thats why the lats arent ever listed as being involved in it. you should have stipulated slight involvement since they are not as important as you indicated. for those that bench with their shoulders retracted, high chest, even less involvement. only time i see someone recruit thier lats to such an extreme is with poor form when they over protract at the top of the movement when they over rotate the shoulder for that "extra" at the top. that movement is actually a means of training the pec minor directly.
as for getting back to the topic of this thread as to why the lats are sore; isometrically contracting hard and even contraction with a controlled release throughout a press is to blame.