Of course there's nothing wrong with asking for a trade. Kevin Garnett played for 13 season in Minesotta before getting the call from Danny Ainge. Karl Malone, Gary Payton, Clyde Drexler and Chuck ALL tried winning with other teams. But these were established players that tried winning for their own franchises before giving up and going to South Beach. I think what LeBron did was a total d!ck move. And I'm glad Cleveland got Kyrie Irving. But LBJ got his team to the Finals and made them the best regular season team in the NBA two years in a row!
And of course Melo and CP3 did stuff for the Nuggets and Hornets. But neither ever made their teams legitimate title contenders like LeBron did. And as a matter of fact, it wasn't until the Nuggets traded for Chauncey Billups in 2007 that the Nuggets even made it out of the first round! Melo averaged significantly less during the 07-08 than in previous years by the way.
NO didn't surround Paul with a legit #2 his entire time there. He did all that was asked of him really before getting traded. Plus NO had to trade him since he was going to be a FA after this season anyways and would likely leave. So instead of leaving and getting nothing in return, they got solid picks and young talent, though Gordon has proven to be injury prone and a flake.
LeBron was a Free Agent, he had free reign to go where he wanted and owed Cleveland nothing. The more time goes on the less harsh I feel about him leaving Cleveland. He never asked to be traded. He played out his contract and left on his own.
Melo was also approaching FA I think, and it's not like Denver got nothing in return for him. They probably pulled the biggest return of all of these teams with solid pieces (Gallo, Chandler, Mozgov) that could yield them better results than the Melo-led teams did.
tl;dr. It's hard for me to feel any sort of ill will towards a guy that asks for a trade respectfully or plays out his contract before leaving. Have no respect for guys that pout, are drama queens, etc (Dwight).