Well you are wrong. Sudden death would begin if the first team fails to score, the second team would only need a field goal to win.
From a rule implementation standpoint, you are wrong.
In sudden death, the first team to score wins. This means that there is no extra-point attempt after a touchdown.
Under the rule I suggested, if the first team did not score and the second team scored a TD, the second team would still have to execute an extra-point attempt, for exactly the same reason that you (currently) still attempt a PAT if you score a winning TD with 0:00 remaining in the 4th quarter.
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