When do you split the files? How do you track which data resides in which files? Does one file represent one kind of data (table)? Does it reflect data within a given time range? Do you sometimes need to retrieve data that crosses file boundaries?
You quickly lose the simplicity inherent in saving to just a single file.
Which is where Sqlite shines. It's a single file. But with a full, user defined schema. And can update it and query it incrementally, without having to read and write the entire thing frequently. It handles all of that complexity for you.