> As long as a company isn't somehow forcing me to use it services, I'm free to go elsewhere.
You might want to educate yourself on an economic concept called network effects:
https://en.wikipedia.org/wiki/Network_effect
> The fact that you desire something from Google that it isn't giving you (searching with more privacy, better free email service, whatever) doesn't give you some sort of moral claim against the company.
Doesn't that depend on what it is that you expect and which role Google (or any other company or person) plays in withholding whatever it is that you do expect from you?
> The public can vote for other companies by buying from or using them.
Well, yes, it can, and one way to implement that is by organizing a government that enforces it, no?
If your argument is that people can do so through independent individual decisions: Well, to some degree they can, but even then I don't see why they necessarily should? If Google, say, can organize a ton of people to work unified towards its goals, why shouldn't the public at large do the same?
But I guess more importantly: To a large degree, you actually can't. Where network effects or scaling efficiencies are involved, there are many situations in which it would be a huge sacrifice with extremely high risk to individually decide against the (quasi-)monopoly, even though overall society would be better off if many people did. In such situations, coordination between actors is required to achieve the better outcome for everyone. That is a role that government can play: To enable coordination between members of a public in order to reach the critical mass that is necessary to move from a (quasi-)monopolistic equilibrium to the overall better equilibrium of multiple competing offers.