This is where I bring up that Blackbeard shat his pants at the "Dark King" and ran away with his tail between his legs.
It's cope to argue that current Blackbeard stands a chance against Prime Rayleigh when he ran away from Old Rayleigh.
Yeah, exaggerating as usual.
Blackbeard already considering the scenario of letting Hancock go, even
before Rayleigh came.
Teach: "Do you really think if I let her go... she's going to be nice and turn everyone back to normal?"
Koby: "If she doesn't turn the soldiers back to normal... It will be a big problem. Hah... Hah..."
Hancock: "I will do it if you all leave the island...!! Ugh."
Teach squeezes Hancock's neck tighter.
Teach: "And... that is a lie!! The moment I let you go, you will turn us into stone. And that will be our end, right? To be honest, I think there's no way a man can't be affected by your powers. It's a difficult situation... So I think I should just kill you."
He just wasn't sure Hancock would actually turn his mates back even if he let her go.
Then Rayleigh came to guarantee it.
Rayleigh coming is surely a factor, but it is not like Blackbeard ran away just because old Rayleigh came.
- he already considered of letting Hancock go with returning his petrified crewmates as exchange (not sure if he will keep his word though, and sure, Rayleigh being here guarantees he keeps his words)
- before leaving, he got his request fulfilled: curing petrified mates
- Rayleigh is biggest factor, but there is also Shakky the former Kuja Queen, Hancock who is still alive, and 2 SSG whose power shocked Teach before.
So it is not like "old Rayleigh alone made Blackbeard run away like bitch".