I'll put it this way to help you out.
My computer has 4 GB of RAM. That means it can store, in RAM, 4 billion letters. That's roughly 7 million complete novels. In RAM. At once. All 7 million novels can be loaded into memory and unloaded in around 2 seconds. I haven't met a person who can memorize and forget the contents of 7 million novels in 2 seconds.
With one hard drive I can do this 250 times. My hard drive has a data throughput of around 171,000 novels a second. So to fill my memory completely from the hard drive it would take about 41 seconds. I haven't met a person who could read 171,000 novels in one second.
Of course, this information is sweetened when you consider how a well-written algorithm would function. Would it have to read the entire contents of the file? No, the file would have to meet certain criteria first. A computer with an NTFS filesystem can assess the criteria of roughly 300,000 files a second. I don't know about you but I can't read and evaluate 300,000 file access timestamps a second.
A great thing about using a computer, though, is how parallel it is. I can have one thread reading metadata and evaluating the file for a later stage; if it passes the first thread, I can have one thread loading it into memory and another thread analysing the contents of the file simultaneously. The best part about it, though? You can have this program running constantly, 24/7, continually scanning the filesystem for files to archive or delete. It doesn't need to sleep. It doesn't need to take a break. It doesn't need a salary (or worse, hourly wages), and it doesn't need benefits. It's also literally millions, if not billions of times faster than a human doing the same task.
Also, honestly, if your story is ruined because the main character can't be a guy who sits around all day deleting stuff then it's going to be a pretty boring story.