See, in recent years, I've thought of Matt as a double-edged sword; they're screwed with him, but they'd likely be somewhat screwed without him. For some, he still is the draw to the show. Frankly, as much as his image has been tarnished, NBC just doesn't have a successor that could easily fill the void. Installing Josh would come across to many as the show being desperate (which it would be). Carson is the poor man's Seacrest, and to think we thought HE might get hired, you can forget Daly. Personally, I think Lester is better than the weekday show. The slower-paced weekend show fits him well, and it could be argued that much of it has been shaped around him. Honestly, their best bet right now is Willie, but flat out dumping Lauer for ANYONE would likely cause some short-term damage. And with how NBC is being run these days, Matt's successor would likely be vilified by many, and the new guy wouldn't stand a chance against management. Matt would have to be given a really good deal (yes, maybe even pricier than his current contract) to leave voluntarily, or maybe he just wakes up one day and resigns, but his exit would have to be his own (possibly provoked) choice.
Frankly, they're stuck.