"They don't. Follow the money: why do ads power free services? The advertiser needs to expect to make more money in the scenario where they run the ad as compared to where they don't. The viewer must be spending more money in response to having seen it"

The first part is true, the second part pretty obviously isn't. Advertizers expect to net $ from ad buys, but most advertising isn't trying to increase a consumers total spending, its trying to drive that spending towards the companies products.

To give the most obvious example, the largest category of advertising is for food and beverage products. But no one thinks that if those ads all suddenly disappeared, people would stop buying food.

That makes sense, though you're still paying for the service or product that includes advertising as part of buying the third party product such as a beverage. If you can't afford the service or product then you're down to off-brand products that don't run ads