Caleb D. answered 07/27/19
Simple Explanations
Yes, it is a bit silly this is allowed. As you've checked the CIL for it, I'm sure you're aware that properties are literally methods. You aren't partially overriding the property as much as you're only overriding the hidden "string TestProperty_get()" method while not overriding the hidden "void TestProperty_set(string value)" method. Property methods are no different from any other method in the runtime, and it's only by C#'s syntatic sugar do properties pretend to be variables.
As for practical application, yes. There may be scenarios where you only want or need to override only the getter or setter, such as adding an observer pattern to the setter while leaving the getter as-is.