[dragonwriter]

> But if a small board game company sends an influencer a free board game, an influencer is not allowed to review it.

Yes, they are, they aren’t allowed to fail to disclose the fact of the donation when reviewing it.

> Personally, I think having "background" props is much more insidious.

The FTC has power to deal with deceptive, not with insidious (the latter is dubious as a power of government at all under the First Amendment, but its clearly not, whether or not within the power of government broadly, not something Congress has by statute assigned to the FTC the way they have dealing with deceptive trade practices.)