In a vacuum, I honestly thought trading LeBron might have been the best move for Cleveland's future once Kyrie made his trade demand (this assumes that reports about the Cavs feeling that LeBron is likely leaving are true). Irving is younger, less of a prima dona than LeBron is, is 100 times more clutch than LeBron will ever be, is under contract for an additional year, and seemingly just wanted to be the man *somewhere* - not necessarily in the biggest market. 
Quick aside, but I remember LeBron's first year back in Cleveland after he returned, I was reading one of the Cavs blogs, and there were some posters that were already fed up with LeBron, his immaturity and all the baggage and politics that accompany him wherever he goes. They wanted to trade him then. They were obviously in the minority, but I give credit to them for calling him out then. 
I don't know what the Cavs could have gotten in exchange for LeBron, but as long as the other team had a feeling it could extend or re-sign LeBron, the Cavs probably would have gotten a lot more in return than they did in exchange for Irving. 
While LeBron has a NTC, if the club had approached him and said (in a more diplomatic way), "We're sick of dealing with you and the way you hold us hostage, we plan to build around Kyrie, and we're looking to trade you," I think that would've burned the bridge to such an extent that LeBron would have waived his NTC for a select few teams. So I do think it would've been feasible to trade him as long as one of his select teams was willing/able to make a deal. 
That being said, the public backlash against Dan Gilbert would've been an absolute nightmare. LeBron is worshipped by the vast majority of Cavs fans, and LeBron's PR team would've made him out to be the victim and Gilbert out to be the villain, and Cavs fans would've totally bought that. 
So while it may have been the best option for the Cavs to take, and a more realistic option than some may think, I don't think the team could have risked the backlash.