It's not so simple...

So you don't think that Safari and Chrome would use two separate engines if they hadn't started from a common, open source code base?

And the fact that you say "gecko" not "firefox" is nothing to do with the code being open source? Would you be able to choose from dozens of free browsers (midoria, galeon, epiphany etc.) and know they're render the page well because they use one of the same two engines? Would all those projects be able to rely on well-tested, standard-compliant engines if those engines weren't open source? Wouldn't they all have their own, buggy engines with slightly different behaviour, or just not exist at all?

If the browser market was split into lots of different engines no single one would ever have competed with IE's dominance, and web designers would have continued to write for IE only. The fact that gecko and webkit have a significant share, and MS were forced to make IE more standards compliant, is partly due their use in multiple different browsers, which is possible because they are open source.