PageB's hidden field will only contain data relevant to PageB.
In your scenario, what if I were in Page B prior to my visit in Page A? Then When I come back to Page B, this page has no state, because no state of no page is saved on the session (i.e., on the server).
But when I was in Page B on the 1st time, I did change its state to be different than its default state. So where was it saved in your algorithm?