There are two reasons why Air Mauritius would not be welcome in the Star Alliance. Firstly, both SAA and Singapore Airlines already ply the Indian Ocean, and they wouldn't want the cake to be divided up any further.

Secondly, Air Mauritius sell Australia-UK Business Class airfares from around US$2800. Airlines like Singapore and Thai would not want to see their frequent flyers move their business to Air Mauritius while continuing to earn status with them.