There's no question of whether a business
can exist without targeted advertising ("invasive" advertising). But they're definitely going to use it whenever feasible, because it's the most efficient form, possibly more than direct marketing.
The ways a business can make money online are A) partnerships, B) advertising, C) goods/services, D) subscriptions, or E) community. The last two are dwarfed by the first three, which depend on advertising. Even if you're a B2B, you still need marketing to get new clients, which almost invariably includes some kind of advertising.
So the majority of websites people visit are still paid for with some form of marketing. It may be indirect, such as by affiliate, partnership, selling of private data, etc, or it may be direct, such as with advertisements and spam/newsletters. The user is still going to pay for it, one way or another. If they're not paying via a subscription or donation, they're paying through their use as a marketing target. (And often, via both!)