Are people really following the strategy of doing nothing? Do you really think it hurts your candidacy to not follow up and show your enthusiasm towards the program? How about having a current or former student write a letter on your behalf?
I've got to believe that this can't hurt, but at the same time the Adcom has been very clear that it will not take any additional information into consideration as part of the application. So if your friend / alumni / current student knows people in admissions, this might work. Otherwise, the letter may end up in the trash. Either way, I wouldn't think that they would penalize you for showing enthusiasm. They haven't said "please do not contact us," only "we are unable to accept..."
It'd be interesting to gain some insight from a current student... perhaps one with Adcom interaction / experience...