A important point that programmers often overlook is that even writing a buggy but large software and managed to finished it with a lot of functionalities is fundamentally hard than a writing simple program. So unless you really are much better than them (and even so you need to make sure you are the only one actually going to rewrite it, which unlikely), you will have small chance doing better.

However there is a time rewrite is a good solution, that is when you find a lot of the functionalities the old code base provides are NOT actually needed. In this case, it is perfect (and you should rewrite it), because you are writing a much simpler software and you have a much greater chance of success.