Uber estimated that it costs Waymo $2/mile to operate.
Google says they charge $1.60 to $2.60 a mile, depending on location and demand, so Waymo is already almost certainly at the price you claim you'd be taking it.
I think you dramatically underestimate how much it actually costs to operate a car. Most people think they pay $0 to garage their car, for instance, since the cost was rolled into the price of their house purchase and mostly invisible. But it isn't $0 to a business. Likewise, very few people depreciate their car over just 5 years. Or clean it inside and out every single day.
Here's one attempt at costs for Waymo that finds it costs them about $60,000 a year to operate a single car. Also notice the comments talking about how the per vehicle price is high, how that flows into higher insurance, and all kinds of other things.
https://www.reddit.com/r/waymo/comments/1il5d5i/unit_costs_p...
Maybe someday there will be a discount AV taxi company using 10 year old beat up Honda Civics that only get cleaned once a month and provide extremely barebones support to pull the costs down to $1/mile. That's a 50% drop in costs from today, so hard to see it coming very quickly. But that's still pretty expensive to be using as a daily commuter!
And note that the IRS per mile rate is $0.70/mile. It's not perfect but it is a decent third party estimate of the true cost of operating a car. Hard to see any taxi company charging anything less than that. So a 10 mile commute every day is still going to cost you $280/month in an AV taxi for the foreseeable future.