The startup is growing and you have now 5 full-time devs on your team. You have an older application which is up and running in production and a new web application almost ready to be released. You have something like 5 physical servers (some new, some outdated), and 5/10 "cloud machines". The old version of your application was running to a simple webserver and evolved overtime to something more "professional". On the other hand, your new application takes profit of the cloud environment and is designed to support "high traffic volume" by using queues, nosql and other cool stuffs... Your sales are increasing, features development and bug fixing are needed. Your devs are at 110% of their capacity (and become real "Software swiss army knife developers") by developing a new app and supporting the old one... As you run out of resources, when it comes to resolve specifics problems, you call "a guy who knows" by paying expensive bills. You have unix and windows servers and you install updates and read the log viewer when you have the time or when you get an application error. So far, an ordinary situation for a tech startup...
So, now you have the picture. Should this company hire a sys admin or let the "devs who want" time to operate the infrastructure and outsource when they have doubt about the solution ??
Only you can truly answer this question.
How much time do your devs spend in total doing the sys admin work?
Of course there may be some other benefits (other than purely monetary) of having someone in house. You need to decide if they are important enough to pay for at this stage.