Many of the open source projects mentioned already have a pretty strong vested financial interest behind them. They are no longer true open source projects.
I think it's natural for popular open source projects to eventually turn into businesses but I think there is a point where they really shouldn't be considered 'open source' any more and Mozilla is definitely one of them.
I think the word you're having more of an issue with isn't 'open source', but defining what exactly a 'project' is vs. a business. On that latter point, I would agree with you that a project doesn't seem as much of a 'project' when most of the core people are employed to work on it towards specific goals the funders have designated.
As long as the source is open under a permissive licence they are open source.
If someone has figured out a way to make a profit model around it - I would say, that is a bonus as it entails support for a long time and guarantees end-user-valuable goals driving the project.
I think the consumers of the open source software must be responsible to ensure financial health of those projects and not tax payers. Simply because in such cases more useful projects would thrive where as bad projects would die out quickly.
The last thing I want to hear is that Mozila called Bill Clinton for a lecture paid him $1M and later Hillary gave a grant of $100M of my money to Mozilla. That is how governments works.