Well, you know, Patreon could do that. Its a way for Content Creators like those on YouTube to let their contributers offer them money for content, livestreams and more.
The only problem is that Patreon may be a way for TekSyndicate to create content and buy stuff, but their time is still valuable. An experienced and skilled programmer can ear a six figure salary a year (over 100,000$ US dollars), easily. So while Patreon might be a way for us to help them pay for products, that doesn't take into account the time they're setting aside (that they could be working) to script, shoot, edit, realize a mistake and re-shoot and/or correct said mistake, re-edit, upload, and hope neither the compression fudged something up, nor the recording itself wasn't harmed (because of hardware damage, overheating, lack of storage or low battery), or that the upload stream didn't get corrupted mid-upload, or some other error.
So with that in mind, note that the documentary that TekSyndicate wants to make costs 60,000$. We haven't even reached 1,500$ of that yet. So would Patreon help? Yes, if Logan, Pistol, Qain, Wendell and that-other-guy-that-just-got-hired-whose-name-I-can't-remember-for-pounds-of-bacon (sorry person I'm referring to) could spend dozens of hours a week (which they could be working and earning more money that way to) for the Tek for what probably wouldn't even be minimum wage. 1,500$ / (12 hours a week x 4.2 weeks a month x five people) = ~5.95$/h
That's a full dollar an hour less than minimum wage for their time, and we haven't even got to their cost of living, recording equipment, shooting videos because they have them before they're released (so the videos can come out on the product's release date), purchasing the hardware, or even paying for shipping. The fact that Linus can afford staff even with the funding from his forum members and help from sponsors like Intel, Corsair, ASUS and others is nothing short of a small miracle!
So while this idea is nice, you'd need a whole lot more money coming from Patreon. Although maybe Patreon might be a way that TekSyndicate could give back to the community. Maybe a Patreon giveaway, and offer LiveStreams that are exclusive for Patreon contributors? Perhaps also move TekSupport into being the same thing as the Patreon thing, so that way all Patreon contributors get no ads on the forum and some nice stuff.
(Maybe also add a few other things. Like paying for international shipping, although if the winner is from overseas than the next product to be reviewed and then shipped to some other lucky winner might be delayed because of shipping costs depending on the product. And that also includes taxes, like Brazil's ridiculous 100% imported goods tax.)