> Will your next workplace value all the effort you spent that way?

I'd hope so - as it's reasonable to assume that a next role for someone already managing/leading would involve more management/leadership. So yes, skills/achievements/examples in that area should be valued.

> Are the servant tasks even what you want to spend your time with?

It's probably not for everyone; but if someone doesn't want to perform the tasks that (many would say) are necessary to be a good manager/leader, maybe they shouldn't be in a manager/leader position in the first place?