personally i feel like a map is necessary for a good platformsplorey game. the idea is once i cant progress in the current path im going, i can teleport to somewhere else where there's a lot of empty squares nearby and start exploring new squares. people say metroidvanias are known for their backtracking, but a good metroidvania built in this way shouldn't have much backtracking.
aus does this quite well in my opinion, you can often choose multiple directions to go (up, down, left or right) though it can be quite difficult to see what i mean if you already know the layout like we do