The reason that no-tip restaurants charge the surcharges is so that they can keep their menu prices on par with restaurants that do expect tips. If you have to up your prices by 20% compared to your competitor, suddenly your restaurant goes from seeming like a casual-date-night place (based on the menu price) to a the-folks-are-in-town place, or from a folks-are-in-town place to an anniversary-dinner place. It’s not the most logical thing in the world but it does reflect how people price restaurants when they’re deciding where to eat.
(I read an article quite a while ago on one of the trendsetting living-wage, no-tip rerstaurants where the owner straight up said that when they tried the model without the surcharge they lost tons of business due to the menu prices, but diners at least understood that the surcharge stood in place of a tip. This place was aggressively no-tips though, as in signs that read “any gratuities left at the table will be donated to local charities”.)
Whether a place does indeed do something ethical with the 20% surcharge is a separate question, though if they “don’t accept tips” then that suggests that they’d be bound to pay their employees at least standard minimum wage. At least theoretically. The place in the faintly-remembered article claimed to just use the surcharge income on staff salaries.