That's a good move to use server hardware. The upside of a server is really the Operating System though. It just makes a lot of sense to use it. For example, Server 2012R2 Essentials can handle remote access, domain users and groups (essential for security), remote web access, server backup (as well as a backup of every other computer on your network), VPN, reports and monitoring via email, fax, and much more.
The increased complexity stems from people trying to do more than they would normally do. Obviously there is more of a possibility for issues when you see all the stuff it can do. But the reality is you would've never had those abilities if you didn't have the server OS in the first place. A lot of people mention issues with the security groups and stuff like that, but if you look at P2P. Most people just allow Everyone access to the AC folder meaning anyone can get access to it. You can do the same with a server, but why would you want to? You have centralized user management so you make an account on the server and that person can log into every computer on the network rather than making separate accounts, folders, files, shortcuts, etc. Disabling access is extremely simple too. I might so a web series on this if people are interested.
It's also good look at new technologies with virtualization. Replicating servers can be had for very affordable prices now. You can use any old desktop or a used server from eBay.