The HD DVD add-on did not fail miserably, you might want to do at least SOME research before spouting off false claims. First, the add-on had sold 150K units in the US after 2 months (which was more than Toshiba branded HD DVD players had sold in 6 months) at the $200 price point. The add-on sold over 316K units in the US by the time it ended (which is pretty good considering the relative failure of HD DVD). How was it a terrible idea? It gave people a cheap way to watch HD DVD movies (since HD DVD players were much more expensive). It was a good idea, and you can't claim it was a bad idea just because HD DVD failed.
Microsoft didn't want to delay the Xbox 360 just to add in HD DVD support (the first HD DVD player came out 5 months after the Xbox 360 launch). Microsoft, it obviously seems, was more concerned about hurting Sony than supporting one format. There were credible reports though that Microsoft was preparing to announce a Xbox 360 with the HD DVD player built-in at GDC 2008, but Toshiba announced it was ceasing supporting of the format 2 months earlier at CES.
As for calling it cheap, that is my bad. I forgot that it launched at $200. It was not ultra-cheap, but it was still much cheaper than regular HD DVD players (like how the PlayStation 3 was the cheapest Blu-ray Disc player for a long time).