Here are my reasons why they wont.
In an interview, Sangakkara was asked how to play against "tremendous Mendis". He said that at first it was fairly tough, but after a while in the nets against him, it became much easier.
In the Asia Cup, in the match Sri Lanka played against India before the final, Sri lanka benched Mendis. This was because their plan was to make sure that India haven't played against him a lot thus making it harder for India, and their plan worked
If they let him play in all their matches, India will very soon learn to play against him much easier making him more ineffective. I feel Mendis is sort of like Lasinth Malinga. At first, no one knew how to play against him and he became a very effective bowler, so Sri lanka let him play all the matches, but after a while, he became largely ineffective. In the 2 test in Australia and the home series with England, Malinga didn't do well at all and now he is hardly ever included in the squad.
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