I grant that the necessary statekeeping is technically possible with enough spiritual commitment, yes, but would repeat my entreatment to ask whether it should be done just because it can be done.
Nothing to do with "RFC purity", just a question of best-practical solution with fewest failure modes, given that the objectives are to solve well-known problems (topology hiding, UDP fragmentation) to which there exist well-known, time-tested and standards-compliant solutions.