First of all, to my knowledge there is no truly free market economy on earth today. It's questionable as to whether there ever has been. But I would point to a country like Singapore as one fairly good example according to what I've heard. Also, in general what is billed as "privatization" these days is really a government assisted monopoly given to a private company.
This is the justification for all the privitisation that has been happening in Australia and elsewhere in the world on the energy, water, banking and telecommunications industries especially.
You realize that the alternative is that all those are owned by the State, with little or more likely no choice regarding service. And that service would most likely be paid for in taxes that everyone would have to pay for, including those who do not use the service and those who are opposed to it. See above regarding privatization.
It sounds good in theory but in reality what motivation do companies with an already large market share ever have to reduce the end price of a product to consumers?
Competition. And the ever expanding democratization of technology.
They spend huge amounts of money on advertising to brand themselves so that they can maintain high prices and higher margins.
True, but you'll notice that is usually the established brands that spend most of their time doing this. But does Coke really need to advertise at this point? It's rather asinine. I have debated whether the abolishment of the corporation (a legal fiction facilitated by the government) would be required in order to have a truly free market.
Coke is the most expensive soft drink here by far and yet is still the market leader.
Soft drinks here in the US are among the most cheap products available. Even cheaper than water in some cases.
Prices very rarely go down in any sector
Cell phones and computers are industries that have become radically cheaper to the point that they are basically expendable.
if the taxation burden is reduced or erased companies would only pass on a fraction of that savings to the consumer and the from my limited knowledge of economics the increase money supply would have inflationary pressure
Taxation takes money from everyone's pocket. Businesses have to pass the cost of taxes on to you through higher prices or a reduced quality product or service. With the money I had taken out every month from taxes last year I could have made 2/3s of my rent or both my insurance payments, food and whatever gear I wanted to buy. But the greatest problem with taxes as I said earlier is that generally everyone pays regardless of whether they use the service or whether they are opposed to it.
Hope this answers your questions, I can expound on it more if you wish.