The importance of the acceptance of punishment for such disobedience was stressed by the original practitioners, e.g. MLK and Gandhi (not by those in power). Do you expect people to take your argument seriously if you dismiss the reasoning of these famous minds out-of-hand?
Just on general considerations, it's amusing to subordinate our thinking to "famous minds" on a topic like "disobedience". Any ahistorical misunderstandings about these Famous Minds aside, you evaluate a tactic on its effectiveness. If a particular masochistic, submissive tactic furthers your goals, it's worth considering. (Though so are the costs.) Otherwise, it's plainly absurd.
As MLK himself would've no doubt pointed out, there were others participating in the Civil Rights movement. These movements aren't reduceable to the famous minds of Great Leaders, though of course those in power (who want people to obey leaders) try to frame history that peculiar way.
I am not assuming these famous minds are correct, I am saying you won't get people to listen to you if you dismiss these famous minds as obviously wrong with a 4 sentence comment.
Please, update your notions of civil disobedience in history. MLK and Gandhi drew on historical predecessors who, despite not being called civil disobedients, were very much that and are considered and referenced by philosophers and political theorists as such. MLK and Gandhi were not the "original practitioners". Moreover, even if they were the first civil disobedients, there is nothing about the status of first that indicates greater authority to defining or adequately justifying disobedient acts.
I've been enjoying your comments throughout this thread a good deal, because you raise a lot of great points of discussion. But it appears that, in total, you're very distracted by the likes of MLK and Gandhi, and it's somewhat preventing considering things from a higher, more abstract level where you can reason about civil disobedience itself, pulled apart from the particulars of how some disobedients have practiced it.
MLK and Gandhi did not submit to punishment as a method to convince others to join them in disobedience. (This would be rather counterproductive, wouldn't it?) They did it to draw attention to injustice from the public, the vast majority of whom would not join them in disobedience.
MLK and Gandhi did not make the moral claim that the punishment was just--they would say the opposite--they claimed that their own actions were only just because they accepted this (unjust) punishment.
EDIT (reply to grimtrigger): You would argue, then, that MLK's followers (or their followers' followers) would be justified in fleeing? I don't think so.
No, my point isn't that they submitted to punishment as a method to convince other to join them.
My point is that they Accepting submitting to punisment as a method to convince others to join them.
Lets say they did what Snowden did and fled the country. Both may of had the means, but their potential constituencies did not. MLK/Ghandi said "I'll stick around and accept the punishment, because thats a path others can follow".
It wasn't MLK or Ghandi breaking the law that changed anything. It was their millions of supporters breaking the law that had the effect.