The downside is power consumption due to the combination of more data converters and additional digital processing required for each antenna, in comparison to phase shifters and gain control implemented at RF together with analog combining- which can then be done with a single ADC (for receiver) and DAC (for transmitter). Consider how dynamic power across the capacitance of every gate grows as $P= C V^2 f$. (Also motivating lower voltage solutions!). Highly integrated RF MMIC solutions are becoming available which are compelling when power dissipation is an ultimate concern.
When power dissipation and cost is not a concern, the performance and flexibility of an all digital solution would be very attractive.