There are several problems with making something mandatory for availing something as basic as a mobile phone connection. In today's world, it is almost akin to a right to have a mobile phone, if you wish to be connected with the world. Most (actually all) existing connections already were verified at the residence of the subscriber while giving it to you. So asking for a mandatory link to Aadhaar makes little sense. Old people or some other segments may see it as a harassment. Other options like passport etc. should be provided, if at all a further ID is required.
Except for one or two things -maybe providing one while filing returns- there are many other ways to find out the identity of a person. Biometric ID is not foolproof, as the introduction of Iris scans proves.
More research on the downside with different segments is needed, and a guarantee of no leaks/misuse is necessary before making everyone get one compulsorily.