This same question came up in a forum I frequent, and just like I said there, I'd wonder if Microsoft really wants to fight a two front war in the console and handheld markets. I think they should focus on achieving profits with the XBox 360 before they create another potential money sink.
Of course, they could just say "Look how much of a success Sony has had in just over a year of entering the market!" Well, depending on whose numbers you trust, Sony's PSP could be a good example of a true challenger to the king of the handheld world. By some accounts Sony owns roughly 25% of the market. I think that 25% is only compared to the market it shares with the Nintendo DS, because I don't think the PSP owns 25% of the global handheld market when you consider all the people who still have the older Gameboy Advances, SPs, etc., which numbers in the tens of millions.
Also, there is still the Japanese market. As the last two Microsoft console launches there have shown, reception by the Japanese was lackluster at best. I think for a true challenger to Sony and Nintendo, a Microsoft handheld would really have to succeed in Japan. Sure, many people will say "But Europe and the Americas are Microsoft's main market," but I think this is a limited view. Microsoft does see Japan as a market it must penetrate successfully, which is why they began courting more Japanese companies to create games that cater more to the Japanese people.
Also, Japan is a significant market for games. Over there, the Nintendo DS sold 4 million units in 2005, twice that of the PSP for the same year. If you look at the sales charts for the past several months, every week was basically 6 - 7 DS games in the top 10 sales chart. On the other hand, it was incredibly rare to see a PSP game crack the top 10 of the chart.
And that is also something that Microsoft should learn from. The PSP sells well in the States and Europe probably because it is seen as cooler, more stylish, and it has more capabilities than the admittedly plain-jane DS. However, in my very humble opinion, its game selection is more limited than the DS's. Microsoft could really make an impact if they deliver with a steady stream of good, quality games and not rely on whatever other features their handheld would have (i.e. Sony's UMDs being more popular than the actual games).
Microsoft should also learn that having the most powerful parts does not make a system inherently better than another. At its core, the PSP is more powerful than the DS (dual MIPS 300 MHz processors (locked at 200 Mhz max), more powerful graphics engine), but the DS, at least in Japan, has sold more. Why? Even with a relatively weaker system, the games being developed for it are fun and appealing to more than just the 18-35 demographic. That's why games like the Brain Training games have been so successful and continue to stay on the charts.
Microsoft can make this work, but they might have to shift some of their views.