Part of me thinks, well, maybe they could just split the difference and make the display an opt-outable feature.
But I think the genie is well out of the bottle at this point. We now inhabit a world in which a lot of people make their livings based on Twitter fanbase reach (or, really, on the public display thereof, given that they're not actually capable of engaging every single follower with every single tweet). And I think there'd be an interesting psychological game afoot if various people started opting out of the display. Would others see that as some sort of admission of lower status? Would they see it as somehow antisocial? Personally speaking, I think it would be a nice feature to have, and I wouldn't care about who did and did not display his counts. But if I've learned anything in my life, it's that my preferences are atypical.
I suspect it wouldn't work -- due in some part to vanity, and in a large part to the well established social-psychological phenomenon of "social proof." As a species, we like things that are popular. Conversely, we are hesitant to sample things, let alone subscribe to them, until they've been validated by others. Ideally, we seek things that have been validated by others of high social status. But in a pinch, validation by a large number of people will do the trick.
We keep social score. And, even if we don't consciously realize or even accept it, we want others to know our own score.
I tend to agree with most of your points, though. As you very eloquently put it, our natural tendency is to accumulate noise -- even if we claim to want signal clarity. Google+'s circles are a great attempt to let us have our cake (noise) and eat it, too (signal). But over time, I imagine that the act of constant social curation and message-filtering will grow more tiresome than it's worth for many users. That's just a hunch, and it's totally unsubstantiated by any data I have, or could ever hope to get my hands on. At least for now.