Wow I did not know that, I was always under the assumption that I needed to have a project using the Microsoft.NET.Sdk.Web for anything Web as its base. Thanks for the info!
Starting with 3.0 (or 5.0?) they ditched the Startup class and just added in everything by default. Much easier for the regular web application. The modular approach is still everywhere though. You can just pick the components you need, most of them also run without DI, it's just a bit of a hassle to manage all those dependencies manually.