NAND flash program/erase cycles
You are not the first to have this worry, so there has been a lot of work put into "wear levelling" (good search term) to ensure that your much abused 1KB file doesn't wear the drive out after only 1000 edits.

Indeed, in the extreme case that it's the only content of the drive, you could make 32 million edits to it and the wear levelling software would distribute it evenly across the drive, so those 32 million edits would count as one program/erase cycle.

There's a bit more to it, the directory information needs to go somewhere too, and a badly designed file system could overwrite and wear out the directory blocks sooner than this, but I think the filesystems are better designed than that.

If anyone knows specific defects or problems along these lines, such as a file system to avoid with flash drives, I'd be curious to hear about them too - but wear levelling to avoid the problem is the basic idea.