I don't agree. The more likely outcome would be complete domination of big brands because they own the mindshare (e.g. people will remember Amazon.co.uk, they will not remember hundreds of small businesses too).
Even if you were not directly influenced by advertising, you probably were indirectly through word of mouth.
(I do think advertising is net positive and prohibiting it would be a bad idea: https://www.jefftk.com/p/effect-of-advertising)