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Firefox is on the brink of being dropped by the US Government
(www.brycewray.com)
This is a most excellent place for technology news and articles.
The Free Software Foundation Europe has an awesome initiative called Public Money Public Code where they try to convince lawmakers to use as much open source software as possible when using public funds. I really hope they succeed.
What about security? If it's open source, anyone can poke around in the code and find vulnerabilities to exploit way easier.
Tell me you have never worked in IT security without telling me you never worked in IT security.
To give you an actual answer, instead of pure Internet snark, the concept you're proposing is called "security through obscurity" if you want to research it.
The TL:DR of it is it doesn't work. If it did, all software would be proprietary and things like viruses wouldn't exist. The source code for Windows isn't available, but Windows gets exploited constantly.