You say that "a business with a monopoly can raise the cost of their product to the price the market can bear" which seems to be exactly what Google has achieved with their competitive pricing model. If they charged more then they would lose buisiness. If they charged less they'd be leaving money on the table. This leaves no room for a competitor and therefore it is a monopoly, both in theory and in practice no matter how hard you want to argue against it.

While Google monetizes its core web properties such as google, gmail, and youtube via a closed advertising system. That doesn't mean the worth of the company is held in AdWords. If Google decided to shutter AdWords and use a third party the third party would still need to pay billions per year for exclusivity.

However, Google does leverage their ad business into non-google properties via vertical integration eg. I can buy ads on CNN via AdWords but I can't buy ads on Google search from DataXu or other DSPs.

They do have a monopoly in search. If they decide to delist you, you're f*cked.