I understand and appreciate your comment but was wondering whether there is a technical reason why Mu or BP should need to reside in root.
As far as I remember, there was always a risk of things not working if it was run from a directory, either in Mu/BP it/themselves or perhaps with plugins but I am no longer sure why or what. (I am coming back a bit to both after looking at other things).
Basically – and notwithstanding your SEO comment – I would prefer having any CMS in a directory to give me the freedom to have whatever I may choose on the root index page.