Header bidding is designed to expose the clearing price of exchange and SSP auctions so that a publisher’s technology can make an informed decision about which ad to serve. These prices are pitted against each other as well as the publisher’s demand from their primary ad server (usually Doubleclick).
In a perfect world all of this would be done on the server side. The primary benefit would be reduced payload size and lower latency in the browser. It’s not likely to happen, however. It would require SSPs, exchanges and ad servers to figure out how to work with each other in a server-to-server relationship. These companies tend to be competitors; count that as a business reason that will prevent a server side solution.
Additionally, Real-Time Bidding (RTB) is already a server side auction with discrete buy-side demand sources simultaneously bidding on inventory. It is very likely that a server-side header bidding solution would just end up looking exactly like RTB. And, once again, client side header-header bidding would probably come about to try and take advantage of the disparate server-side header bidding solutions.