Glad I could help! I'm not with Esri though... just an average user like many others 🙂
The GIS Services setup program is one of two that comprise ArcGIS Server for the Microsoft .NET Framework, and it includes the Server Object Manager (SOM) and the Server Object Container (SOC), among other things. These are required to publish services, so the answer is "yes, it is essential".
It sounds like, after installing the NetFx3ServerFeatures feature, you were able to install the NetFX3 feature without issue and that ArcGIS Server now installs just fine since .NET 3.5 is present. It would be awesome if you could mark the correct answer with the green check.