While despoiling Earth is one concern raised by Musk and Hawking it’s not the only one. Other’s include preventing destruction of the species (or at least any civilization) by our own hand through war, or by cataclysmic natural event such as a large meteor strike or super volcano explosion. The argument is that whether by our hand or nature the odds will catch up with us eventually.
As for who will get to go I don’t think it will be viewed all that wonderful a privilege. Life on Mars will not be any utopia. Humans will likely have to live in caves underground, or domed villages. Conditions are likely to be primitive, difficult with even brutal hardships faced by colonists.
An interesting question is how a Mars colony will be governed and whether it will declare its independence from any Earth governance.