I want to be able to request static .html files which are located in
the ~/Views folder.
Well you can. The marked answer is not entirely correct, although it gives a solution.
The reasoning in the marked answer is correct, it is web.config (BlockViewHandler setting to be specific) in the Views folder that prevents the files to be accessed directly. It is there for securing the views in Asp.Net MVC. But if you asked a question about serving these files directly then you likely have a valid reason to do so, like using AngularJS partial views (as in our case) where we do not want to duplicate the views folder with weird names.
So here is a very simple tweak you can do in the web.config file found in the Views folder, without compromising security of your asp.net mvc views. This will secure the .cshtml files as usual but leave your .html files alone.A
Change this
<add name="BlockViewHandler" path="*" verb="*" preCondition="integratedMode" type="System.Web.HttpNotFoundHandler" />
--to--
<add name="BlockViewHandler" path="*.cshtml" verb="*" preCondition="integratedMode" type="System.Web.HttpNotFoundHandler" />