I remember an incident when I was in training, in the circuit as P1S, on base and about to turn for final when a plane suddenly appeared out of the haze on finals, same level, no radio call and seemingly unaware.
I pulled, added power and watched him go underneath, my instructor didn't see him until after as he was watching a plane clearing the runway, we did a 360 and landed after, my instructor spoke to the pilot (and his instructor), wrong frequency calls and they were also watching the clearing plane.
Bad airmanship? Radio frequency was a simple mistake, the clearing plane was definitely a distraction, only two holes in the cheese but they very nearly lined up, a split second later and I would have been looking in the direction of the turn and who knows.
This was in a supercub with radio and few radio aids, I also spent a lot of hours in an Auster with no aids and a hand held when flying into fields that required a radio.
Compulsory TCAS equipment isn't going to be viable in much of the permit to fly categories, primarily due to cost.
Mk1 eyeball is still the best tool, accepting there are limitations and that other folk don't always do what you expect.