those projects shouldn’t really exist
You think web browsers should not exist? How do you write Google Chrome, and all of it's dependencies, in one page of code?
I think you're miss-understanding the article. Joel didn't say you should never rewrite an individual component in your code, he was saying you should never throw out an entire project (all of the components) and start from scratch.
He also wasn't talking about "multiple people and man-years of work". He was talking much larger projects. How many people have contributed Chrome? Not just direct contributions writing lines of code, but indirect contributions such as reporting bugs or writing documentation on how it works?
If Google were to start over, all of that would be thrown out. It just can't be done.
All you can really do is what Microsoft did with IE / Edge. Edge was a fork of Chromium which was a fork of WebKit which was a fork of KTHML which was a fork of the KDE HTML Widget. Which dates back to 1996. Internet Explorer started in 1995. Microsoft didn't start Edge from scratch, they basically shifted their team of developers over to another project that was the same age.
The smaller the project, the easier it is to do a full rewrite but realistically it's almost never a good idea unless your product is very young.