I am sorry, but that generalization merits some sources. Can you give me some examples of Microsoft buying a cross platform tool and shutting it down. Mind you I think you are inferring they purchase to eliminate competition. Not a situation where they buy something like Groove, run with it for a bit, see that it is not getting traction and then kill the product.
Lets turn it around though, can you give some examples of Microsoft buying a cross platform tool and continuing to support multiple platforms with it?
I cannot think of any offhand.
I dont think they necessarily purchased it to eliminate the competition exactly, there is likely something about the tech that they really like/want. or maybe it is the people involved.
My wild guess is that they love the ability to target other mobile platforms easily, and will continue to support that. I do predict though that over time they will discontinue/shutdown/slowdown/disable the ability to develop for those multiple mobile platforms on Mac OS X and Linux. ie, that their goal in this case will be to persuade developers that they should be developing for all mobile platforms on Windows, using C#