Just because they have the money, doesn't mean they would take any deal. Think of all the companies they could buy with a $100bn+; they prefer to hold cash at -2% real return.
Expected returns are the crucial factor here. Alphabet is sharing risks, waiting for better opportunities to deploy the cash.
There's a realization that beating services like Uber and Lyft on cost per ride (to undercut on price) will be hard and require significant capital without a clear path to sustained profitability. The economics aren't hard to understand:
You can either pay one person (out of a - growing- pool of tens of millions of willing drivers) ~$15 an hour (depending on geography) in a $20k car or you can pay very little per hour in a 250k for the car + a gigantic engineering team + compute infrastructure. It can make sense on a large scale, but it'll be hard to do.
Alphabet is sitting on a golden goose: their ad & search business (and the network they've built around that) is the perfect monopoly. Close to unbreakable and getting stronger over time (you won't be able to build a better search engine than Google unless you have as much data as Google). Why would they dilute their superb EBIT margins, rapid growth and extreme salability with the low-margin, ultra-high competition ride-sharing market?
Think of paying a driver as renting compute on a extremely capable vision processing, decision making, robotic driver that costs you very little. As unemployment (eventually) increases again, the market will be flooded with unbelievable amounts of idle human minds.
There's a general theme here: It's not enough to teach a computer to do something as good as a human, you have to undercut on price as well. For this reason, I believe that hair dressers have less to fear from automation than Radiologists.
The "we need to sell to a third party so that our shareholders can figure out the valuation of this division"-argument is mute because it isn't applied to the countless other parts of Alphabet (or any other company). E.g. Youtube and Google Cloud can be valued based on financial data given to the SEC, though I admit, sometimes spinoffs do unlock value.