Even if you're just using a regular expression for parsing, it can be worth moving the parsing code to its own function and testing it like a parser.
In java land when I'm writing stuff i use unit tests mostly as a place where i can run code without having to compile the whole app. And any tests that come out of it just end up being a bit of regression protection. But there's always a bigger slightly more complex unit test i write which tests the bigger unit of function. And those really straddle the line between unit and integration testing but i find i get the most value from them because one you lock in and publish functionality you have a contract you have to honor.
I agree with the grandparent that they are more useful as a project matures rather than the design stage. Starting small and adding tests as designs solidify is a good tradeoff.