A question about youtube videos and various browsers ...

I'm a tad curious as I find the following inconsistency a bit frustrating.

If I was browsing on Youtube and decided to embed a video here, why is it that using the mobile version of a link confuses desktop browsers and sends the desktop browser to some kind of Youtube limbo page which has nothing to do with the embedded video in the first place?

If I was on my Kindle or smartphone, if I came across a desktop version of a Youtube video, there will be an error message indicating the browser incompatibility and a direct link provided to the mobile version of the video. My main question is why isn't the opposite reciprocated for desktop browsers? Easy peasy. No problem. One more click and I'm watching the video on my mobile device.

But why when using a full desktop browser when encountering a mobile link to a mobile version of Youtube video isn't there a reciprocal link directing the browser to the full desktop version of the video? One would think that full sized browsers would have less trouble dealing with these situations then mobile browsers....