You're kidding, right? nGage and Gizmondo and a host of others push Vita well off the top-spot for biggest handheld failure.
It is true though they were not coming from the company that used to be the leading force in the game entertainment business.
Anyway I think there is a market for handheld but it is getting more and more centered toward pretty low end hardware with a matching price.
I still think that the PSV is too powerful too pricey, now will it get better with the PS4 launch, I don't know. I expect it to sell a tad better but not enough to make a massive difference in the number of publishers interested in the platform when the gaming mobile market already generates more revenues than the handheld one.
WRT to MSFT launching a handheld in some form, I think they won't, if they were to do it I think they would fail, not because the market is too tiny, supposedly owned by Nintendo, etc. I think they would fail because the product would not be properly positioned, for me the golden price in its age of cheap tablets and omnipresent smart phone might be 99$, you could go further that but I think that it would discard the product as an impulse present for kids for lots of parents (or casuals).
Now costumers are likely to have another device they can play with even if the experience is of lesser quality.
If tomorrow MSFT launch a 99$ handheld, running some form of winphone8, runs the same games, allow cross platform gaming on social games, and follow up with quality games, I'm not sure it would fail, especially if it can interact in some way with the XB1 in some ways (streaming from the XB1 or cross platform gaming on casual games).
Now if they try to sell an "Apple like product", what SOny tried with the PSV, they will fail.
Anyway I don't think they will (or in a reactive manner if some form of Android handhelds were to gain traction, actually following that line of thinking I wonder if they would be better off trying to be pro active on that front).