a cat that will come at most times will not come near you when they are hurt or scared
It depends. I had cats who came to me when they were sick or injured as they knew from past experiences that me or the vet could help make the pain goes away.
As for now, one of my cats has glaucoma and she comes to me when I'm late for her eyedrops but only for one of the two kinds she got 4 times a day.
She doesn't like the other kind of eyedrops and she run away when the time comes. But recently I got feet surgery and I'm not walking too well. She still tends to run away but when I beg her to stop as I'm not able to chase her, she freezes and let herself be picked up without resistance.
If you want to put yourself on the map, publish your own map.