This was something we were seriously considering on our (now cancelled) mission, and the general scientific consensus after lengthy research was “OH HELL NO.”
Remember that we do not consistently have the luxury of beaming to the moon from the most convenient place on earth. For (USA) lunar missions, we beam from 3 earth stations (Canberra, someplace in the US, and I forget). Canberra was the far one, so you’re limited first by the top possible totally secured speed to Canberra + whatever time to the moon and back + speed back from Canberra + network latency + satellites are hard. Our math booked the entire deal at around 4.5 seconds round-trip.
