You deal with peak demand by having a supply that is equal to the peak. Automatic Rideshare companies can self balance over a large area, watch the predictable trends that show up during a year and so on and will print money and thus have a lot of capital.

You're also forgetting that most existing cars on the road have way more seating capacity than needed, since they need to account for the maximum number of people who will use that car at once. A family of four needs a car with four seats, even if most of the time that car will only be carrying one person to work and back throughout the week. Self driving cars will be much more efficient in that respect.

That assumes that nearby places have different peak times, which is probably a flawed assumption.

By offering discounted fares at off-peak times, and charging premium fares at the busiest times, you can smooth out the peaks while optimising profitability.

Easy, only companies with absurd amounts of cash will be able to compete, and won't mind burning through billions to dominate the market. The economics of Uber and Lyft don't work right now, but that isn't stopping them.

Google, Uber, GM, and whoever else will compete with one or two heavily funded startups, until one wins and the rest fail because of the dynamics you describe.

So I think the GP has the wrong picture.

No until they control the market at which point you will pay all the subsidy back with interest.

It's not impossible, but if they go into corrupt regulation (how else could they do it?) there is no reason they can't get the same without the throwing a lot of money away first. So, again, they won't.

Also, you make it sound like corrupt, industry protecting regulation is the exception and not the norm. Where do you live, and does this fantasy place accept immigrants?

Most vehicles sit idle in a parking lot but could be doing meaningful work.

(Queue SitCom script where someone tries to leave a party but forgot to turn off the feature and their car won't be back for 30 minutes...)

I would guess that in most cities the capacity is not limited by capital to buy cars, but capacity of the street network, which cars, autonomous or not, are notoriously bad at utilizing.

Many rides aren't so time sensitive that they can't be shifted to another time if the price is right (or wrong).

Car sharing companies will likely come up with a subscription service where you pay $X/month for your normal commute, then they can make sure they have enough base capacity for the regular rides and the on-demand rides can use demand pricing to ensure that everyone can get a car when they need it.