I'm not American and don't live in America, so I guess you need to rethink that bit. Companies are clearly not people. If they were, they wouldn't be able to go jurisdictional shopping so easily.
Taxation without representation is pretty widely recognised as problematic though. Not for nothing did it help trigger the war of independence against in the colonies against the British. Think about it: if you can't influence politicians in any way, what stops them taxing 100% of your labour? The only thing that stops governments doing this at the moment is the fear of consequences from their citizens: either at the ballot box in democracies or at the hands of the mob in dictatorships. Companies can't vote and they can't rebel, so there has to be some kind of pressure that pushes back against ever higher taxation. Usually this is indirect: countries fear that if they tax companies too much, they'll go bust, people will lose their jobs, and then those people will vote.
But when companies are largely distributed and a government doesn't feel any real exposure via their own population, the natural tendency is to say "if you want to sell to our citizens, you have to pay us lots of tax" and there's not much a company can do about it except simply deny an entire population their services, which is about as useful a response as a person deciding the best way to lower their tax bill is to throw themselves off a bridge. Nobody wins in this situation!
> In my view, companies (and their investors) have the privilege of being able to profit by providing services to citizens, and they should pay (be taxed) for this privilege.
Since when is the ability to make a profit by engaging in trade a "privilege"? People were doing that in the earliest tribes and farming settlements where the closest thing to a government was the local alpha male. The privilege of taxation is one people grant to governments in return for the stability and ability to make long term plans that they provide; but that privilege can be revoked and has been throughout history.