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Personally I'm on the fence about whether it should be banned. There are several possible down-sides.
First, it would be very hard for new players to enter a marketplace if there was no advertising allowed. Traditional brand-recognition would be everything. It would benefit the largest players in the market, similar to how the UK's ban on tobacco advertising actually helped the established tobacco firms.
Second, it would be impossible to enforce. They would sneak it in with paid endorsements, so while there would be no "overt" advertising, it would just massively boost the "advertorial" market. So you no longer have "advertising", you have "advercontent" and that's all the content you have, because nobody can afford to make anything else.
Third, if you're using a free service and are annoyed that there are adverts, so you want to ban them, then, hello, welcome to the new improved world where this service just doesn't exist in the first place.
EDIT: fourth, if it applied to something like video game advertising, then that would mean the types of games that cost a lot to produce just aren't economically viable anymore. No more GTA V type games, and massive layoffs. The same with filmmaking. But it'll also crash the indie market.
I've thought about these things as well, but ultimately I don't think it's worth it compared to the harm and expense advertisement creates (not just for the companies as you mentioned, but also the collective burden of wasting social product wasted on industry together with the personal harm inflicted on people by the industry).
For the first point, since the general tendency under industrial capitalism in most sectors is toward domination by a cartel or monopoly, with or without an advertisement ban, I think there's something bigger at stake than just one more marginal factor that slows or accelerates that. This is why in my mind that argument reduces to whether or not advertisement is worthwhile for the sake of encouraging new markets, which would depend on how a person feels about unsustainable growth, artificially induced demand for crap people don't need, and our ramshackle economic structure that falls apart if the rent-seeking rich holding the world hostage don't earn their 4% per annum or whatever (weighed against the genuine benefit of new products toward overall well-being).
With enforcement, I don't think it would be very difficult. All that would really be required is framing the law in such a way that advertisement is considered an anti-competitive practice vulnerable to litigation from other firms in the industry. I think the international copyright and patent regime makes a good comparison; it's a completely artificial and unnatural creation impossible to maintain without imposing the threat of state punishment, with complicated and blurry as hell legal definitions that often get enforced arbitrarily, but it more or less works (for its purpose) because the rights can be enforced with weaponized litigation from the companies themselves.
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The free digital service thing is another interesting point. You mention this:
Third, if you're using a free service and are annoyed that there are adverts, so you want to ban them, then, hello, welcome to the new improved world where this service just doesn't exist in the first place.
-- and I have to wonder, is that actually a bad thing? Should things like youtube, facebook, etc exist? Hindsight is 20/20, and it's a stretch to say that we should have banned advertisement so that these things never formed, but really, I think things would be better without them.
I think youtube is maybe the best example to consider. The question is really a technical one: is there any compelling reason why we should do all of our video sharing over the internet through a single centralized multinational corporation's monopoly? Do we need their servers to do this? I don't think we do.
If advertisements were banned and the "user-created content platform" model was basically impossible to make profitable, people would still want to share videos over the internet. The incredible usefulness of the internet would have still stimulated increases in bandwidth and networking technology. The difference is that instead of a monopoly or cartel buying up obscene amounts of server space so they can control everything, we'd probably instead have a decentralized system for these "user networks" like youtube, facebook, etc. We would probably have improved peer-to-peer protocols written and improved by academics and non-profits with the sole aim of improving usefulness (with no profit motive required), rather than closed-door research done by Google or whoever to ever expand their control and entrench their userbase which is conditional on their profit from doing so.
But again, hindsight is 20/20, and it would be outrageous to think that we should have anticipated this and banned advertisement of all things as the solution, and obviously it's too late to ever happen anyway. But I still think things would be better without it.
Edit:
Really though, what gets me when thinking about advertisements is imagining life without them. The world be be a much less physically ugly place to live in, it would be easier to enjoy and take part in cultural work, and I think the market itself would have a better chance of standing on merit. It's particularly damning in my mind to think that the primary purpose of advertisement isn't even to communicate any useful information, but only to impart a psychological impression that creates superficial recognition and the illusion of trustworthiness. What seems to me to be many dubious economic effects along with this is just a complement to the personal harm I think it creates.