They have never needed to tear apart the mountain to work on the Yeti. They've
been working on the Yeti. It's very close to ground level, actually; and even if they hadn't built access routes to it (they did), the bits of the mountain that would have to be torn out are all entirely unthemed and backstage. That's never been the issue.
The issues have been generally known for a long time. They've just never been acknowledged directly, by Joe or Disney or anyone involved. Because there does not exist a clean answer that doesn't potentially pin blame on one party or another. This is my current understanding of the situation.
The story is of two different and separate companies; Imagineering and Operations. Imagineering sold and supplied a product to Operations, a ridiculously cool Yeti animatronic, for a very substantial sum of money. That Yeti had significant issues, primarily with the amount of weight consistently being applied to the swinging arm, requiring lots of upkeep and B-mode downtime.
@HandsomePete said it earlier - if failure is even a possibility, no one involved wants an already unfathomably heavy arm being launched downwards into the ride track with the force of a jet engine. So Disco Yeti it is.
Imagineering says that Operations didn't properly maintain the figure, Operations says that Imagineering sold them a faulty product. There do exist solutions, and likely they've existed for a long while now. But they would be time-consuming and extremely expensive - and neither company wants to foot that bill.
But even if one company or another took ownership and agreed to fund the project, what would be the upside? Maybe seven seconds of cool factor?
The real issue why the Yeti will probably never be fixed is that it doesn't need to be. The effect is insanely cool. An absolutely stunning piece of machinery and storytelling combined - but the ride has been without the yeti for the vast majority of its' existence, and guests still come off the attraction singing its' praises. They still reride, they still give it high GSAT scores, they still think the Yeti is really,
really cool; even if it doesn't move. The vast majority have never even seen it move, or know that it ever was supposed to.
The effect is dazzling, but ultimately superfluous, immaterial to whether people enjoy the attraction or not. Rhode, Imagineering, and Operations had their shot to sneak the A-Mode Yeti through the door past the executives' glares, and they let it fall and break the moment they got past the doorframe. There is no way anyone on top is willing to pay multiple millions of (additional) dollars for an original attraction to recreate an effect that no one that matters actually cares that much about.
It's deeply unfortunate, but again, that's my current understanding. If anyone has knowledge that contradicts this, I would be genuinely interested to hear it.