The red tape is needed for legal reasons. As a company you can't just throw around money via Paypal, gofundme or whatever, the risk is too high that it will end up being a tax/audit problem.
Give a company a proper bill with VAT, and they'll stuff you with money.
Companies make charitable donations. I wonder if there's a charity that accepts donations for specific projects. If not, is there a good reason why?
Companies make charitable donations to entities registered with the tax authorities as charities. When a donation is scrutinised during an audit its clear what its for, based on the receiving entity. A random payment to a person looks like a bribe or some suspicious activity when its not in direct exchange for goods or services. This will require an explanation to the person conducting the audit at the very least.
BS corporate red tape is a reality, though. So why not offer workarounds that help them give you money?
As mentioned above, offer consulting services and accept corporate purchase orders. Be able to give and receive PO numbers. This is the language the bean counters speak, and sprinkles magic pixie dust on your invoices, ensuring you get paid.
One really big downside to offering this yourself or providing it as a service: contracts. You can try avoid paying a lawyer and use a standard contract. The engineering manager would be cool with that since he just wants to support a project but all bets are off when it hits legal. A big enough company and you can get into a seemingly endless revision back-and-forth that can last weeks. No big deal for them and other big companies they work with since they have salaried lawyers on staff but the cost is something to consider for everyone else.
Hiring a lawyer is important if you are going to be contracting with a large enough company though. The money you save and the time you spend as a result of having a competent lawyer draft, negotiate, and proof your contracts pays for itself in the long run when, inevitably, something goes wrong on a project.
What makes it BS? Can you come up with a better way to manage giving access to a bank account with hundreds of millions of dollars to a thousand people?
If they don’t accomplish the goal (and they don’t), you can hardly call them “effective”.
Are they? Usually unless you're known, they bring in next to nothing.