I think either end of the spectrum is fine: highly skilled / can do your job if needed, or not technically skilled at all / honest about it / tracks schedule / delegates all technical authority. The messy middle is where the problems happen.
You can't be a coach and a player. It doesn't work. Having technical skills and being able to make or weigh in on big picture decisions is great. But you have to trust your team to do their job, even if it isn't exactly how you would do it. Does it meet the business need? Does it make sense strategically. Is your team staying unblocked? Are you being reactive or proactive? Are your team members growing and improving?
I disagree. My best bosses have been player/coaches. You usually only find this at smaller companies.