By the way Akon also came to india to sing for SRK movie. May be Indian music directors like to experiment. Atif is not main stream. Few songs like flavor of the month.
I totally agree with you, it does make sense, just because Pakistani singers come to India doesn't mean that they are desperate. The music industry is a fast growing industry and to be successful you have to answer to the demand of your costumers, in the case of Atif, he is mainly popular with the younger generation and I also listen to his song myself on a regularly basis while my parents hate his songs. And the fact that Pakistani singers are invited means that there is demand for other than the Indian music. The Indian music industry is mainly focused on Bollywood songs while other kind of music is not fully promoted,...at least that's my impression of it, I don't actually know how popular other music forms are in India,...I am personally more inclined towards the band and sufi music than Bollywood music. The other thing is that the Pakistani singers are already very well established overseas,...and I guess, it is safer and easier to invest in them then to start from scratch and having the risk that a new band may not work out as expected, resulting in a financial loss,...Money is the only thing that counts!
It is the same with any other field, people are invited to the West to work, not because they lack people with expertise or aren't capable do their work properly by themself, but because they want to have diversity on the work floor so that they can compete with the ever changing industry. They invite people from different backgrounds, different culture, with different mind-set etc. so that they eventually can make use of their capability consequently leading to a very acceptable profit.