Sort of. The cost of labor is the cost floor of the competition. So long as Waymo et al are smaller than the competition, i.e. so long as they don’t need to compete on price, they should tack under their direction. They aren’t setting the market price.
The moment they need to compete, they can tank the price or increase service quality. (They could also stay put and milk it. But that invites new-entrant competition.)
Internet companies compete on price out the gate because we have low marginal costs. A company like Waymo has hardware costs that make competing on price out the gate prohibitive. So in a sense, their costs don’t have to do with labour. But that’s sort of true for any automation tech.
And believing that this is likely to happen is the problem I have with the whole proposition. I don't see any real player with capital, data and tech know-how to get into this in a way to turn it into a proper competition.