I have to say, this situation has improved enough that I've had no problem using BT controller connection.
We're talking about games like Elden Ring, Enter the Gungeon, MGS:Snake Eater Delta.. and reaction time definitely matters for those games. One controller even came with a 2.4ghz 1000hz dongle, and it seems the new controller will probably have an option like that if the GabeGear has the hardware built into it: "Steam Controller's wireless adapter is built right into Steam Machine for direct pairing."