Should I inline all CSS files programmatically to optimize page load speed?

Inlining all your CSS means it cannot be cached, so every single page load will contain all of the CSS required, and when you are using large libraries that can really be a lot of wasted bandwidth. For example, Bootstrap is around 120k. Note the Google link you shared specifies the following (emphasis mine):

If the external CSS resources are small, you can insert those directly into the HTML document, which is called inlining.

So a single page load may be faster but overall it's likely to be slower.

Personally I would stay away from doing that. However, one thing you can do is bundle all of your CSS into a single request (you are using MVC so that is relatively simple) so you only have to do a single extra trip to the server for your CSS and all future pages requested by the browser will not need to ask for them again.

No one has mentioned the intended use case for this technique, which is definitely not to load 100% of your css. Rather, this technique is meant to make users think the page has loaded faster.

When we discuss making pages load faster, the real goal is generally to make the page load seem faster. From the perspective of the user experience, this is much more important than actually making the load take less time. It doesn't matter if the whole page take 500ms to load, because a human can't parse it that quickly anyway. What matters is how quickly the page appears to have loaded.

So the appropriate usage of this technique is to load, immediately, the absolutely essential css to make the page render properly. That is, there are some css rules that make the images be the right size, that make things float correctly, that avoid that horrible appearance of page content jumping around the page while the facebook SDK finishes its business. That code needs to be present in the same instant the markup is loaded. Solution: inline that critical css.

But definitely DO NOT inline all of the css. There can be another 100kb that loads later, if that css only styles content that is loading asynchronously anyway. But if there is page structure that must be in the correct form after 25ms, that css should be inlined.