I'm not so sure about that. There are plenty of organizations that have money in the bank, yet still get volunteers to support them. They key is the need for reserves.
Wikipedia is free for anyone to use.
I agree that the bluntness of their donation campaign is over the top. But I'm also willing to bet if it was subtle, they wouldn't be at the financial point they are now. In 2007, donations capped at just $2 million.
Reserves are common in nonprofits. Without them, there's nowhere to go than down. But it's also important to note that it's not just about Wikipedia. The campaign supports WMF. Here's the report via Charity Navigator: https://www.charitynavigator.org/index.cfm?bay=search.summary&orgid=11212