The argument for advertising is that it's so difficult for a new entrant to a market to challenge an entrenched incumbent, unless they can advertise.

I honestly don't know if that argument holds water.

Intuitively, I'd say it doesn't hold water: Entrenched incumbents would generally tend to have more money than new competitors, so the incumbent can afford more advertising to drown out that of the challenger.

The only net gain I can see is for the advertising industry, which extracts money from both challenger and incumbent.