Well if you are squeezing the edges why would the centre start getting a lot of contact pressure there - the corners will since they are being pressed together. If you want that then one needs to add something to press it together in the centre (that could be one possible way).
When we bolt something locally you will get a high contact pressure there but not necessarily elsewhere.
See what happens in a flanged connection (figure 7 in the doc. below), where the contact pressure is very local at and around the bolts, but not so much away from them. In the contact pressure you showed, similar things can be seen, so similar phenomena.
Also this is good.