why would he? ... Sweyn had argubly the best claim of any of the pretenders, except for prehaps Edgar which had no support at all at the current time due to his youth. While he might not have had the military to push for the claim himself, he would certainly have no reason to support any of the others, unless he would be very well paid to do so, and i don't think anyone would be willing to cough up the ammount of either gold or land he would want to even consider it.
Sure, Sweyn supported Edgar a few years later, but that was the expectation of running England through him as a puppet king, and he abandoned the idea as soon as William paid him enough to go home, leaving Edgar flundering