The funny thing is, when fans asked why they didn't bother trying to expand more on the other X-Men characters like Kitty Pryde or Cyclops and kept going back to Wolverine even in plots he didn't matter in (DOFP) the answer came down to "Look, if it wasn't for characters like Wolverine the X-Men would've stayed canceled after the 60s. Those older classic characters just aren't worth the effort. We're gonna keep inserting Wolverine cause he's more interesting."
Meanwhile the MCU takes someone who by all rights was as "Boring" as Cyclops like Captain America and makes him now be seen as a proper Icon on par with Superman and Batman.
Yeah, it seems like the MCU is the king of making more obscure characters popular. The X-Men are a treasure trove of characters that are ripe for many different types of stories, and Wolverine is definitely not the reason they've continued to exist. Sure the original Stan Lee comic run was lackluster, and the second group of X-Men were what made it really successful, but even Chris Claremont focused on a lot of different characters in his run, and we've only gotten more diverse casts of characters in X-Men related books since then. FOX thinking that X-Men had to have Wolverine (or a clearly phoning it in Lawrence) to be popular was just a sign of their lack of ability to take something more obscure and work with it.
Whenever the MCU actually fully starts to use the X-men, I bet we're going to see a lot of love for characters and concepts that FOX didn't use just because no one working on the franchise there had the ability or the desire to use, and it will probably make Disney/Marvel even more billions of dollars.