Russian asylum will alleviate both issues: It gives him easier access to commercial flights, and it makes it politically far more difficult for those European states that for example were willing to prevent Morales' plane access on a mere rumour he was aboard to justify forcing down a plane he is on. Consider the political fallout if an Aeroflot plane with someone granted political asylum by Russia gets turned back.. Or for that matter another diplomatic mission with him aboard their plane with asylum status.
(also noteworthy is that most nations need you to be within their borders before you can apply for asylum. It appears Snowden would much rather have an invite before he arrives. This is ruling out most destinations)
> they simply have to arrive and claim asylum
In order to arrive, he needs the travel document.