I think it depends. There are times in my life when I've wanted a tool and looked for existing products, contributed a few patches and been happy.

Then there are other times when there was nothing like what I wanted out there already. So I had to start from scratch. (My console-based mail-client, with Lua scripting is a prime example.)

Sometimes even knowing there are similar things out there it makes sense to write your own, for learning, for specific features that you know upstream would never support, etc. (Yes, I wrote another static-site generator. In perl. I also wrote a perl-based cfengine-like server-automation tool.)

In the abstract contributing to existing code might make sense. But for personal, or contractual reasons, it isn't unreasonable to set out on your own path.