Putin's fleet has a big issue getting to Suez.
While there's agreements for access through the Bosphorus, there was an agreement about not threatening Ukraine too, so closing it to him would be even.
Gas was a big issue a decade ago. Not so much now. The important thing is to avoid giving him credit for increasing prices, although I would expect all gas from such a relatively dodgy locale coming through a restrictive pipe to be bought on very long-term contracts.