There are two main disadvantages of satellite communication.
The first is cost. Developing, launching and maintaining a satellite is extremely expensive. No further explanation of that is necessary.
The second is the time delay in responding.
Communications satellites are typically positioned so they rotate around the earth at the same rotation rate as the earth. This is called 'geosynchronous' positioning.
The geosynchronous orbit is far from earth, so the time it takes for the signal to reach the satellite and then bounce back to earth is about half a second.
The delays can be very annoying on voice calls, as people tend to talk over each other.
The delays are also problem with data exchange, as data response packets are also delayed which limits the effective bandwidth of the channel.
One way broadcasts, like TV and Radio signals are perfect for satellites as no response is required.