To break away from spending months on pieces before they are mastered often people need to rethink their approach to their piano studies.
...it's very possible to learn to play a new work in a week, but I realize that at least for me it won't be note perfect and there will be a few details missing or fudged. Does that still count as master? If not, wouldn't learning to play a piece at mastery still take a similar amount of time, if it is at a level challenging for you?
I guess the level measured which constitutes mastery is different for everyone. I think a few missed detailed and uncontrolled expression in places cannot be at a level which would represent a failed exam result.
If it takes someone a week to learn something which otherwise someone else could sight read immediately I am not sure if that would also represent masterful rate of learning.
I guess we can consider it critical thinking/reading - applying what has been read, learned previously to the present piece.
I'm thinking of something like a Chopin waltz (I always keep using this as a benchmark lol). I think that, with a decent amount of effort, it's possible to play a Chopin waltz in a week from memory, with maybe the occasional slip. Would it pass an exam? Possibly, if you're good.
I get your point about sightreading ability, but I think it should be pointed out that there is considerable room for improvement even when it comes to memorizing pieces. And at least for me, memory hasn't had as much to do with sightreading as it has had to do with comprehension, for lack of a better word.