So with a 400 degree temperature change on a 1/4 of inch thick skillet bottom there is approximately .006 of an inch of movement.
Skillets are more like 3/32" or a little more in thickness on the bottom. Go ahead and break your best skillet and check the bottom thickness. I bet you would be amazed at how thin the pan really is on the good, older pans.
When I see sellers stating the pan "sits flat" it really doesn't tell me anything other than there may be no wobble when set on a surface (that may not even be flat?). There could be 1/4" upwards warp and the pan will still "sit flat" and have "no wobble". I like to check with a good straight edge. Getting sellers to understand exactly what you want to know is near impossible unless you run across an engineer or machinist selling the pan.
My observations over the years on thousands of skillets do not show me that larger skillets are more bowed or warped than smaller ones although, once you get down to about a No.6 size skillet, the pans do seem to be warped less frequently. I think most warpage comes from rapid and uneven heating and cooling. My mom had an early small TM 10 Griswold skillet that was bowed unevenly downward which I would have to saw was caused by uneven heating at one or more times.
If you sight across a pan's surface you can usually see any bows. If I can't see any up or downward crown or bow or high or low areas the pan is good enough even without measuring although measuring with a straight edge may still show some bowing.
A pan's bottom should not extend in any part below the heat rim. Or, is a flat bottom skillet I like to keep any bow less than 1/16" and I think that is reasonable if the bow is uniform over then bottom and not concentrated in a smaller area.
You can find skillets with Perfectly Flat bottoms in any size and can fine NOS pans with slight bows. I'm not sure that any shrinkage at the time of manufacture when the pan cools is the cause of bowing when new but it could be. Would be interesting to see the pattern and mold that my slant/E No.8 skillet was made from/in to see if they had the same bow as the pan does. If not then the pan did bow during cooliing as it still has the original paper label on the bottom.
If you are buying sight unseen you have to impart what you want to know to the seller of the pan and not ask questions such as "does it sit flat" or "wobble". That won't always give you an accurate description of the pan's flatness.
Steve