Nice concept Doğancan, I was regularly thinking about this.
But I believe we can slightly improve it with a date filter because this version might cause some issues.
Say you take a screenshot at 11:59: It will be deleted in a minute. Or you're looking for a screenshot you had just taken yesterday but it's already gone in less than 24 hours.
So if we modify the cronjob (as below), only old enough files will be handled and the new ones will be kept for a while.
`0 12 * * * find ~/Desktop/Screenshots/ -type f -mtime +7 -exec rm -f {} \;`
(mtime +7: modified more than 7 days ago)