Why would a referee without VAR "delay the whistle" until the goal is scored?. I'm convinced he blew it at around 11 seconds, if you look at him after the goal is scored his hands go nowhere near his mouth to actually blow the whistle (and no English referee at that level keeps the whistle in his mouth).Whistle is clearly delayed until just after the goal, the noise you're hearing as a whistle I'm fairly sure is a scream from by the camera. Note the different tone to the whistle just after the "goal".
Other than that I agree - it's a tough situation, but the ref is the only one positioned to take the initiative and sort this out. As @Ben448844 points out, he's clearly delayed the whistle because the flag feels wrong to him, the mistake is not trusting that instinct and initiating a chat with at least one of the ARs.
I don't think either AR has standing to insist on a conference - AR2 has just made an on/offside call and can't be expected to overrule himself on a pass from the opposite touchline, and AR1 has a far worse view than the ref, as well as other reasons to possibly not be looking at the pass. It has to be the ref who decides to delay and work out what happened.
He has seen the flag and blown, then probably immediately thought what the **** have I just done. Been there, have the t-shirt.