We all know Blackbeard is an opportunistic machiavellian character. He also is aware of the recent developments in Wano, and that the situation is about to get more complicated as Big Mom is heading there too.
This leads me to think that Blackbeard has his eyes set on Whole Cake, after all:
-Big Mom has probably taken most of her military power to Wano. She (probably) still underestimates Luffy, but I don’t think she does the same with Kaido. Furthermore, strong members of her crew as Katakuri do not underestimate Luffy the same way she does and probably convinced her to go all in. In any case, Whole Cake won’t be as protected as usual.
-In this place (Whole Cake Island) there are several Poneglyphs, including one of the four leading to Rafael.
-A lot of Big Mom’s subordinates (even the weaker members or the younger children) have Devil Fruits which we know are also a target for Blackbeard Pirates.
All of this makes of Whole Cake Island an opportunity that Blackbbeard will not lose, and if at some point Big Mom is defeated in Wano (which is most certainly going to happen), Blackbeard will go to Whole Cake Island, take whatever he wants, destroy what he does not and diminishing even more the power of this Yonko.
Even if he does not send a huge military power to Whole Cake Island, now we know that in his crew there are two captains with skills which are perfect to infiltration missions: Shiryu (invisibility) and Devon(Kyubi=Shapeshifting), which will make a lot easier to steal the Poneglyph.
As a final note: If Blackbeard does launch an attack over Whole Cake Island, killing or hurting the weaker subordinates or younger children of Big Mom, this would be reason enough to have some kind of cooperation in the future between the Straw Hats and the older Big Mom children such as Charlotte Katakuri.
*Theory by efegoforit