Amateur (ham) radio is certainly legal in India and takes place regularly.
Not being from India, I can only offer an electronics expert's possible explanation.
The vast majority of voice ham radio - VHF, UHF and the HF spectrum - operate by either a 'line of sight' or 'skip' propagation method. Additionally, it's fairly uncommon for ham radio operators to communicate with someone directly overhead - they nearly always are contacting and conversing with someone located at some distance on the horizon from them. These communications leave a clear path which is subject to easy intercept (monitoring).
While hams do use satellite communications, there are relatively few ham satellites and the communications going through them is easily monitored. While satellite phones also use the same radio waves, their communication is intended (and always takes place) with a repeater above the horizon.
What's the meaning of all that? In a nutshell, it's possible for a sat phone to be down in a wide hole (or deep valley), communicating through a satellite passing directly overhead. The 'line of sight' in these cases would not extend to the horizon to any degree. Therefore, these conversations are extremely difficult to monitor, with the notable exception being electronic intelligence (ELINT) aircraft flying overhead or intelligence satellites.
I'm not aware of India having an intelligence satellite or the necessary infrastructure to easily decrypt and intercept the satellite phones' conversations. Know that I'm not implying that India doesn't have the technical knowhow, but I believe that they have much bigger fish to fry and eliminating the legal use of satellite phones is probably an easier method of keeping comms where they can be intercepted and intelligence gleaned from them acted upon.
That's my 2 cents and I'm certainly subject to being wrong about the above conclusions.