Should governments contribute to Open Source?

Open source software is in many ways an accelerator of innovation and has, in my opinion, improved the lives of nearly every person on earth (directly or indirectly, for example: pretty much all software services I can think of rely heavily on OSS).

However, OSS relies on the good will of people and this can often lead to conflict with companies who are trying to turn a profit.

So my question is: Is it in the interest of governments to actively pay people to maintain OSS projects and remove this potential friction so that companies can rely on OSS as infrastructure?

This is a bit of a stab in the dark, so I'm interested in what HN has to say.