The possibility of recounts should not even be a consideration in debating the merits of a national popular vote. No one has ever suggested that the possibility of a recount constitutes a valid reason why state governors or U.S. Senators, for example, should not be elected by a popular vote.
We do and would vote state by state. Each state manages its own election and is prepared to conduct a recount.
The state-by-state winner-take-all system is not a firewall, but instead causes unnecessary fires.