Hi, welcome to Webmaster World.
It's perfectly possible to come up with a script that would do this but there's a reason why all the ones you've encountered use MySQL. If you let visitors leave a comment some of them will write things you don't want to have displayed: spam, abuse, whatever.
So you'll want to be able to delete comments you don't like. That means you'll want to be able to pick those out individually. With a text file based solution this'll get to be a real pain, believe me, whereas with a database it's much easier to sort the sheep from the goats. Also, should you choose that comments should only be displayed once you've read them and decided they're OK, with a database you can have a column that says whather you've checked them, or not.
There's no technical reason why you can't do all this with simple text files, but the code would be inflexible, over-complex and hard to maintain compared to a database solution. Since life is short and most hosting offerings include MySQL these days, you are unlikely to come across a ready-made answer to your request.
Of course, if you want a custom-built script and you are prepared to pay for it...