anonymous posting must be left as is because anonymous posting ... really lowers the barrier of entry for asking a question

That presumes that the only way to keep "the barrier of entry for asking a question" at a desirably low level is to keep anonymous posting as is. I'm pretty sure that's false. We could, for example, implement pemungkah's suggested change -- allow a poster to control whether to allow anonymous responses -- and Anonymous Monk would still be able to post root nodes.

Of course, you're right in saying "anonymous posting is a feature of this site". It would be nice to get a more persuasive argument for why it's a good feature, though. :-)