I don't think that's an example of the "broken window fallacy", actually. It is generally true that people who consume less, are putting less money into the economy, making aggregate demand lower, making the economy overall smaller. This might not necessarily be bad, but it's not the same line of thinking as saying that e.g. "breaking a window" will cause economic improvement.
The analogy is accurate. Breaking windows creates artificial demand, just like advertising. Advertising wants to break your contentment with the status quo, to make you "realize" that you need product X before you can be fully happy again.
This is one-sided. A lot of modern consumer advertising and especially web advertising works this way, but there is also the goal of simply letting someone know a service or product exists (and might fill a need they presently have).
The problem is this is a lot like search on the internet - if Google were "perfect", advertising wouldn't work, because it would always find exactly what you were looking for exactly when you needed it.
> ... if Google were "perfect", advertising wouldn't work, because it would always find exactly what you were looking for exactly when you needed it.
Advertising will always work so long as there is producer surplus[1] in the economy. If firm A and firm B both earn $10 of economic surplus on the purchase of some product, then either supplier will be willing to spend up to $10 to convince a customer to switch from their competitor to their product. If a customer considers the two firms' products to be substitute goods[2], then both products may be "perfect" search results, because the customer doesn't have a preference between them and considers them both to be equivalently useful, which is why Google can extract money from advertisers to show their product first without significantly harming their user experience.
People's consumption does not occur in a vacuum. If I spend less money on going to the movie theatre, I have more money available to buy books. Either way, I'm putting the same amount of money back into the economy.
If you want to know the real significant cause of lowering aggregate demand, look no further than rent-seeking and wealth accumulation. Billionaires aren't going out and buying their proportional share of movies, books, electronic goods, etc. They're using their money to collect rents from securities markets.
Sounds like we need a more precise terminology than a blanket statement of "damaging the economy." The economy still exists after these actions are taken, it has just become a different economy.
Sort of like how healthier individuals "damage the economy" by consuming fewer treatments and pills.