If it weren't for the grants coming from wealthy business owners, archaeologists wouldn't get most of their digs funded. A lot of these business owners grew up hunting artifacts with their dads, and they shared the info with the archies back in their day.
What about today's kids? A lot of their dads are telling them to keep their mouths shut, as the archies of today aren't their friends, and they are trying to destroy their hobby.
If any of today's kids grow up to be wealthy business owners, do you think they will finance ANY digs for the archies? Nope.
Today's archies are destroying their own future due to ignorance and greed. A vast amount of information is lost in this day and age, when people find sites and keep their mouths shut. Recently-discovered artifacts go quietly into private collections, and we all lose.
Of course there are some bad collectors out there, but we have this problem in any hobby and every facet of life. But when today's archies label ALL collectors as "grave robbers," "looters," or "pot hunters," they have just insulted 100% of the people that pay to go to museums to see their work and possibly fund their digs.
Since we can't seem to stop people from driving drunk, should we ban all sober drivers? That's the same type of logic the archies of today use.
The vast majority of archaeology is done as a required precautionary part of a road building/widening, pipeline, or development that occurs on state or federal lands. That's Cultural Resource Management (CRM) archaeology companies that conduct those Phase I through III investigations/explorations. It's funded by the people doing the widening and building. The small sliver of archaeology done otherwise is academic archaeology. Those may have private funding from a corporation or grants that keep them afloat. Often times they are college credit based classes, so the student archaeologists are essentially paying for those excavations. I don't have exact figures, but I'm guessing 80% of archaeology is done via CRM firms. The rest is academic or even more rare, private funded digs. Even so, a college is usually involved with those. And with academic archaeology, a good chunk is just landowners letting the local school conduct excavations on their property.
My old college's archaeology program has been working in one state park for 20 years. The local power company, as part of them being able to set up shop in that area over 20 years ago, agreed to sponsor various local things. The archaeology at the park was one such grant. Alumni contribute heavily to that archaeology program as well.
As far as the archaeologists labeling people as grave robbers, looters, pot hunters, etc., that does happen. I've worked at sites where people would have to camp out on site, because once it became known in the public that we were finding 'good' artifacts, we would have the occasional pot hunter/grave robber try to sneak onto the site once it gets dark. With intact 1000 year-old burials that have grave goods, not a good thing. As with anything, it's definitely a fraction of a percent of people doing things illegally, but because of that, there is a natural distrust. I'm not saying it's right, because I always had the attitude of making friends with your local enthusiasts because they are the ones that know where the best sites are to begin with. Again, not saying it's right, but archaeologists do for the most part feel they are the protectors of history and everything in the ground. That is why you often have that uneasiness with them.
There definitely needs to be better relationships between archaeologists and hobbyists. I don't agree with your funding argument, but I do think if people get a bad taste in their mouth with archaeologists, they may be less likely to share information with them about things they find on their land, etc.