With doom/quake etc, I’ve always set up my controls so that delete + page down (the keys above left/right arrows) would strafe left/right.
I got quite good at using key combos to run forwards, whilst both turning and strafing.
Friends at school (where I first played Doom) didn’t understand why I used separate strafe keys, when I could just press Alt instead like they all did. I guess they hadn’t imagined needing to turn and strafe together, like when circling an opponent. 😀
But by that time, the mouse was taking over as the choice controller for fps games, so my control scheme never seemed to catch on.