Of course, in reality, the escrow may not be enough to remove the bias, but it's an interesting thought.
They use part of this management fee to invest in their brand, so that studies that don't carry the "neutral-study-guarantee" sticker are treated less seriously than those that do.
You pay in taxes, government dispenses research funds, you don't know where the money is from.
Perhaps an independent foundation could work hard at fundraising to become such an escrow but they'd have a heck of a time raising capital to cover the research I imagine.
Theoretically, this would strongly select for products that are safe but for which no one else wants to fund research into the safety of.