The Montreux Convention specifically prohibits “aircraft carriers”. This is the reason Russia has historically played cute naming games by calling their carriers “aircraft-carrying cruisers”, and additionally equips them with missile payloads somewhat comparable to cruisers or destroyers from other countries.

Also, the US is an ally of Turkey, despite currently strained relations. The US conducting a freedom of navigation cruise through the Bosphorus Strait would cause far, far more problems than it would solve at the moment.