Root raised cosine pulse shaping filter
The primary reason that root raised cosine filters are used is because they can be expressed in closed form and they are simple to understand. There are far better root Nyquist filters out there.

Usually they are optimized through least squares or remez exchange to improve stopband attenuation or some other channel specific criterion.

The ISI-free response (obtained through the cascade of a root Nyquist, the channel, and another root Nyquist) is only accurate in a flat channel (although it is also a good approximation in an almost flat channel). The shortcomings of root Nyquist filters have largely been addressed by DMT/OFDM, SC-FDM, and other proposed (and still experimental) technologies. These technologies result in ISI-free responses even for channels that the root Nyquist filters do not.

However, all of this is very dependent on channel models. If you really want to study the advantages and disadvantages then you need to provide a channel model, because the limitations and drawbacks of any method will be dependent on the channel model you are considering.