The issue is that the physical reality of the network and the location of generators and loads is fixed at time of [re-]dispatch. Regardless of how you reconfigure the dispatch mechanism, there is energy that cannot be moved through the network from the wind in the North to the load centres in the South. The only way to avoid that physical reality is to either massively increase the N-S transmission capacity or to put generation capacity closer to load.
Once these generators have been placed where they are and pending extremely challenging network expansion being realised, it will always be the case that some party or set of parties bears the cost of the constraint.
If you moved the ownership and control of the transmission network and all generators into a single operator that was responsible for optimising its operation in near-real-time and that bore all the costs within a single accounting perimeter, it would do more or less what the the existing market based mechanism does: turn off the wind generators and instruct the thermal plants in the South to run instead.
Yes, it's true that in that case there would not be a "market price" paid to wind turbines that actually cannot run, nor would there be a higher re-dispatch price paid to the thermal generator. However the total system cost would still be the same. Even though the wind turbines would "lose" money because they can't run and the thermal plant wouldn't receive its market price for relieving the congestion.
Of course you could argue that this efficient single operator simply wouldn't have built the wind assets in the first place in a location where they often couldn't run but that assumes that the same policy makers who created the current outcome wouldn't have engineered the exact same outcome through the direct control they presumably would have had of the integrated operator. I will note that many American utilities actually are vertically integrated like this (banned in the EU under the Third Energy Package) and they build in the exact same pattern and bear the constraint costs internally.