If demand reduces dynamic pricing will kick in and cut fares.
The question is whether this incident really will cause large numbers to eschew United metal, and bearing in mind it's near monopoly status on some domestic US pairings, whether some customers even can.
Obviously transatlantic there's plenty of real competition to go to, it will be easier, and unless United cuts fares, probably cheaper, for those promising to forego United to do so. Certainly if this backlash does effect reservations I'd expect it to play out on transatlantic and Pacific fares first, since its easiest to find an alternates on those routes.