This topic has been discussed recently in the ML, and some of the suggestions are to introduce a documentation framework like DocBook, dita, or asciibook for longer documentation and to restrain the README files to the minimum needed for people to get going.
Having a plethora of README files one in each component seems excessive to me and does not solve the problem of documentation (in fact it might make it worse) because now we need to decide what goes in the README and what goes in the other documentation solutions.
Again like discussed in other JIRAs I wish if you'd discuss your intentions in the ML before issuing JIRAs. Sometimes it makes sense to immediately create a JIRA when you discover a bug or fix something obvious. But when deciding on a policy like "Every component should have a README" then at a minimum I think it should be discussed in the mailing list to avoid over inflating the already over inflated JIRA issues.