Thanks for the input madao, but I disagree. First of all, I'm not saying sysadmins are going away in any respect, but I do believe that with increased efficiency there will be fewer admins needed for any given business.
I currently support over 150 production systems on Amazon, so your estimation of 10 servers per sysadmin is outdated and inaccurate. Even by Instagram's own admission they manage hundreds of systems with only 5 sysadmins. By your calculation, Instagram would have needed at least double that.