It was already explained why the letter prefixes are "necessary", or at least substantially improve navigation around the airport. As for the letters chosen being non-sensical, in what way? Apart from maybe not looking most logical on a map (that no one uses), how will the choice of these specific letters negatively impact passengers?

The new flow of passengers will be very simple: Check-in (if applicable) at the terminal noted at your ticket, then follow signs for the gate area mentioned on your boarding pass. I can't see how this could be improved. Dropping letters from the gate numbers would only create more confusion, because suddenly you'd have no easy way to tell passengers to go e.g. to F gates before knowing which particular F gate will be asigned to their flight. And no, you can't use terminal number because gates don't correspond to "check-in terminals" 100%, and again, trying to tell passenger that they should "check-in in terminal 5 and head to gates at terminal 4" is no better than the proposed setup, not to mention that it's not supported by data structure of flight data in GDS and other systems (there's just one terminal number).

The same setup as proposed here exists at VIE, which is my home base. You arrive to the airport, head to the terminal noted at your ticket for check-in, then follow the signs to the gate area (C, D, F, G) on your boarding pass - any terminal / gate area combo is allowed (e.g. T3 has departures from C, F and G gates, possibly D too). It's extremely intuitive and I don't encounter dozens of lost passengers confused by why there's no E gates.