Playing a weather team has massive drawbacks.
You often have to use a crappy pokemon that was stuck in NU for most of fourth gen and didn't get anything new.(Except for the abilities boosting their stab attacks, but still.) Then, if you lose the weather wars, you're stuck with MORe crappy pokemon from NU that got nothing new. I mean, look at most of the swift swimmers. Without swift swim, they're not good. Same thing for the chlorophyll pokemon. The sand ones are alright on their own, but they gain the least from sandstorm, apart from excadrill, who is otherwise underwhelming as well. As for hail, it's just terrible across the board. Only the stallers are good, and even they can be beaten down with t-spikes or different weathers.
Therefore, the drawback is: Having to use crappy weather starter, and being vulnerable to loss of weather.