The indirect revenue is real and is, of course, NOT irrelevant. When all is said and done, there's a financial plus side to keeping them open. That is my point. Apparently, you're having a hard time getting it.
Simply employing folks raises indirect revenue-- revenue that is amazingly important during a slow economic recovery-- by providing income to consumers who then provide business to local economies. Moreover, many of those employees provide services that business relies on. I know I have historically relied on NRCS soil data, Census data, USGS Landsat (satellite) data, etc. Without funding, these services cease, which also ceases business that relies on these services.
If this were simply about cost and benefit, it would be a no-brainer: The government would stay open. But it's not. At the end of the day, it's about a lack of money. The government literally does not have the money to pay all its bills. Employee wages, utilities, contractors, etc.-- it can't pay everything, so it has to pick and chose.
Regarding national parks specifically, my guess is that there are serious concerns about liability, maintenance, graffiti, etc. And while I appreciate volunteers wanting to step up and do the right thing, I don't think it's a good idea. I'd imagine it would create all sorts of training, legality, and liability issues.
And, honestly, from a branding standpoint, I don't think it's a good idea either. Under a best case scenario, the success of temporary volunteerism would simply add to the flawed idea that government can be replaced by volunteerism, despite the obvious fact that temporary volunteerism during a temporary government shutdown is obviously not a sustainable, long term solution. And even if it were-- it's obviously not, but just for the sake of argument-- it would simply be a waste of an opportunity to circulate money through wages, as sustaining that level of volunteerism would involve permanently removing a large chunk of folks from employment.
Good luck with the fire season. I'm near Sacramento, so while I'm not that threatened, I'm very well aware of the risks. I was up in the Lakes Basin Recreation Area recently. It was 90 degrees and dry. It's been about 104 multiple times this year, which is about 20 degrees above the average annual high. In fact, the entire month of July was above the annual high. So I know things are pretty rough up in the Sierra. I can't imagine things are much better down where you're at. Hopefully this all ends soon.