Yes, it matters a lot. One of the reasons people want open source is to be able to "fork away" from a popular project, if the leadership team of that project takes a direction that people disagree with. Obviously this goal is impossible to meet, if the project is closed-source, or has an onerous license.

There is another cost that people don't talk about as much, and that is the cost to understand a large, alien codebase enough to be able to understand and change it. If the effort to contribute is too high, you can't get a second group of programmers to rally around the fork, and the new project will fizzle.

As an example, Google understands the economics of code very well. They know that there is little threat to market dominance for them to release Android or Chromium as open source.

It'd be quite a huge and significant step in the web becoming a single stack or implementation, rather than a set of open standards with various interoperable implementations.