Not in this case.
Mathematics resolves unique solutions from multiple constraints.
Politics takes a resolved solution and fractures it into competing alternatives.
No way no how can the two disciplines help each other.
The supreme court justices can't even agree one which circuit courts should consider which conflicting sections of a law with an outdated purpose of protecting black voting rights being applied to hispanics, which are white and not historically repressed at the voting booth.
Nobody agrees that gerrymandering should be rejected, they merely agree that gerrymandering should only apply to further each parties conflicting goals. And there's not just two parties. There are d's, r's, black groups, hispanic groups, state govt turf, fed govt turf, etc.
While your proposal may seem ideal for a map case, the problem is that there are no constraints agreed upon to guide the selection of better or worse maps.
What they're doing here is simply waiting for the ultimate authority to carve out an arbitrary, final solution.
It will not make any sense either and the final reason your proposal fails is just that....your result might be fair, equitable and verifiable. That would disadvantage all of the power players, and so it is not a desirable political solution.
Here’s a workable, but very-likely “unacceptable to established politicians” approach.
The politics in setting up congressional districts involves gerrymandering 435 districts , so looking for “workable” (see “non-workable” below) and randomized gerrymandering constraints involving roads, conjoined properties and some sort of "symmetry" involving 435 districts (covering the US citizen census count) across each of the 50 states – could be done.
“Non Workable” could be defined as a randomized plan subject to some significant -- and increasing -- percentage (5%, 10%, 20%, etc) of Americans objecting …within 30 days …. to a currently extant randomized plan.
As I said, I could do it … but ... established politicians, and their well connected, "happy", constituents; wouldn’t stand for it because every push of my Go button would come up with a totally unique solution.
But then ...
"Not everything needs to be fixed." -- Randy Pausch