IMO Aakash's exclusion by Colonel is totally justified
1.First of all, Chand was employed by Abhiyankar not just as a mere aide, but because he was one of the 'best guides' out there for the mission. When we go to some foreign place, we often hire guides to help us out, then this is Mount Everest, surely you will require the best guide's service in such alien conditions and high altitudes?
2.Initially, when Roongta had appealed to Colonel to come in on the mission in which his both 'NIM candidates' were participating, he had declined the offer in its face, but only and only because Anjali's story had convinced her, he decided to join in as leader.
3.Thirdly, Abhiyankar indeed did leave Anjali out of the rescue mission because it wasn't Mission Everest anymore but surely he must have also got inspired from Anjali's herculean effort to climb alone and reach them, seeing the passion that she had and finding the weather conditions clear on reaching Nasir, he would have been convinced thoroughly that this girl deserves to get what she wants for once. Call it 'favoritism' if you would, but it is perfectly understandable.
4.As someone already pointed out, Abhiyankar and the rest of the team were obviously unaware with Jagat's change of stance regarding Anjali so there's no way Colonel could have had a change of mind in view of Anjali's original mission.
5.I don't think Aakash's exclusion was 'unprofessional', Colonel clearly contacted Roongta over the decison and if Roongta doesn't have a problem, then why would Abhiyankar feel he is creating some disturbance in his work? Roongta only wanted a picture of CC's flag atop the summit, which Chand could have easily clicked as well.
6.Lastly, Abhiyankar is clearly injured and having internal bleeding, in case at some point he gets in some critical condition and is unable to carry on, who do you think will serve as the second best leader? Aakash or Chand?