Disadvantage: No 'off' switch, whatsoever. It's gonna run as long as it's meant to run, and not a moment less.
...under normal circumstances.
Pedant Alert!
But there is a dramatic off-switch. There are explosives along the body of the SRBs that, when activated, split open the SRB causing the pressure in the combustion chamber to quickly drop and the solid propellant to stop burning.
Of course, this is part of the Flight Termination System used in an emergency. It was used after the Challenger accident. In the videos of that tragic accident, you can see the SRBs start to fly off, still under power, until the Range Safety Officer triggers the FTS and the SRBs break apart.
Even more pedantic ...
Solid rocket motors are designed to produce specific thrust curves mostly by varying the geometry of the core. Many are designed to produce a regressive burn (higher thrust at first) because you often need that.
The hobby rockets like I fly usually require air flowing past the fins to be stable so they are designed with high initial thrust so they are going fast enough when leaving the launch rod or rail.
But many of our hobby motors have progressive burns mainly because they are easier to produce, but also for specific situations, for example to reduce drag and stress at lower altitudes where the air is thicker.