Why can't both have the title earned through their respective philosophies on the matter. It seems very dramatic when two equals are trying to decide the fate of the world. The underdog tones can be brought upon with other elements besides the title. We have the potential of Luffy fighting Blackbeard without an Ancient Weapon to back him up, and how powerful Blackbeard already is.
–- Update From New Post Merge ---
The WG owns the pond, and instead of having one fish trying to challenge it, we have another faction trying to overtake that position for their own selfish desires. Unlike Luffy, that's why the parallels between Luffy and Blackbeard can be carried even after Raftel.
What, or how someone becomes the pirate king differs from person to person. For Luffy is freedom, while for Blackbeard is chaos/conquering. It would work well within the themes of both, to have each acquire the title through different means. Luffy, by finishing exploring the world, and Blackbeard by acquiring an Ancient Power, and getting rid of his competition: mainly Shanks and potentially other emperors.
Blackbeard defeating 1-2 emperors would make him the top pirate in terms of how the world views him.
Yes, Luffy will be the one to ultimately do it, that does not mean there cannot be a competitor trying to take advantage of the shift in power.
More than Luffy toppling the government, slowly I can see him being the one that actually prevents someone from sitting on the Empty Throne. He will help getting Im out of there, but will also prevent anyone from taking his place. Which aligns with his concept of freedom.
They all play in that pond though, the fish differ in size, but none of them can solely endanger the owner of the pond.
They differ in what they think the Pirate King represents, sure, the way to become PK is not different for both though, that´s the main point, at least so far.
Unlike DD for example, whose definition of Pirate King was not about reaching Raftel and finding One Piece, a goal he would deem as meaningless, which fits his attitude shown in Jaya really, both Luffy and BB share the same definition of Pirate King, reach Raftel, find One Piece.
So far at least, which is why i have the problem. If Oda, let´s say, actually points out that BB would be ok with becoming his own specific version of Pirate King, for example, like you said, by finding and using an Ancient Weapon, or by other means, sure, that conflict does not inherently exist, though i would still be somewhat disappointed that Luffy has no credible rival for the PK title, since the other Yonkou are basically second tier compared to the Pirate King or the people who have the potential to reach it, and the Supernova´s rivalry is non-existent and has no credibility.
But it would at least prevent the problem of BB failing a certain goal and then doing the next best thing, it´s just Oda has to portray it credibly, which i have pointed out in my post.
Before that, i will not really pretend it´s a done deal, especially when there are a few other points, albeit not as big as this one, that are somewhat problematic to me narrative-wise.