At a ratio of 10:1, at least in my experience, there's no time for those managers to be hands on with the work and keeping their engineering skills current. I don't personally feel that's a problem, but reading other comments on this post it seems like many HN readers do have an issue with engineering managers who don't keep their tech skills sharp.
For the past year I've only had three direct reports, which would have been too few to keep me occupied if I wasn't also acting tech lead.
IMHO, if you want engineering managers who can occasionally do hands-on things, you probably want a ratio around 6/7:1