I suspect it went forward because it was 1936 which meant:
1. USA had an isolationist foreign policy.
2. A lot of the world was going through the Great Depression.
3. Hitler was rebuilding Germany and had other bigger things to worry about such as solidifying his own power and remilitarising the Rhineland.
4. Britain and France were probably too busy trying to fight the depression and worry about Germany as well as Italy's imperial ambitions.
5. Italy – I doubt they cared as they had no interests in that part of the world. And again they were already engaged in expansionism in Ethiopia (then known as Abyssnia).
6. Spain – just starting an nice little civil war that would cause a lot of international grief.
7. The Black Sea is strategically not vital for trading powers like France or UK or USA or Mediteranean powers like Italy or Spain. It's a dead end street that in 1936 led to the closed state of Stalin's USSR, impoverished Persia (Iran) and as such no money to be made. In any case Iran could be easily accessed via established trade routes via Suez Canal or Indian Ocean.
To be honest Black Sea is still not strategically important. It still leads to an economically undeveloped region and it still is a dead end.
And even if the Turks allow the Russians to sail any kind of warships through the Straits, it leads straight to NATO land of the Aegean and Mediterranean with the Greeks,Italians, French and Spaniards controlling all potential routes backed up by USN units of the 6th Fleet (mainly rotational ships).
It's why I say that NATO's coast of the Black Sea is a liability for NATO. It's not strategically important for NATO but it is for the Russians. The Russians are willing to go to war over Ukraine but NATO is not.
If Ukraine agitates too hard and is rolled over by Russia, it will compromise NATOs southern east flank and place the largely disarmed states Hungary, Romania and Bulgaria in a precarious position.
And with Turkey no longer a reliable NATO partner, there is a threat of Bulgaria and Romania's coasts becoming encircled by countries hostile to NATO. This puts both these countries in a more precarious position.
For now the only benefit of US deploying the odd destroyer to the region is to irritate Russia.