Something to create some sense of progress would be cool, like new map areas or some indicator of how high you are.
Alternatively, if the innocent exploration aspect is kept instead, rare and weird blocks/events on a small number of screens would also keep the game fresh for a lot longer.
Right now I think everyone who starts climbing up is hoping for either something to change or some in-game recognition of their progress; if people knew there was nothing up there I doubt anyone would climb so high just for fun.