But there is a move. In fact, multiple countries have done so, although temporarily: https://euobserver.com/migration/130260
Thing is, border control isn't free; it may not be visible for many of us, but there are a lot of people reliant on the openness of our borders for their daily lives. Imagine having to pass a border check on your way to work - that'd be the reality for many EU citizens nowadays if you were to reintroduce country borders.
And would it really solve the problem? What if those migrants just came by boat anyway? What are we going to do, let'em drown?