Yes, a company cannot do whatever they want.
If you want to dump dangerous waste material in the ground on your company premises, the environment agency will fine you.
You cannot fire employees without a reason. They very well may sue you for doing such think and win.
American here. Yes, you can fire employees at any time without cause. The only thing you cannot do is fire someone for being in a protected class. A new boss can't come in and fire everyone wearing a yarmulke, for example, because religion is a protected class. However, the boss can come in and lay off a whole department because they want to outsource that function -- even if that department were predominantly composed of Jews. An employer would be within their rights to layoff employees by pulling names from a hat, although that would be a pretty stupid way to go about it.
Wrongful termination lawsuits in the United States are usually contractual matters. If there is a union contract in place, or an employment contract, the terms of that contract can be litigated. The most common thing is whether severance pay is called for and whether the prescribed amount of severance was paid.
I do however agree that there should be a means to reach customer service for these companies. I blame Google for that in large part - there was never good customer support for Gmail, even though one's email account is a critical piece of infrastructure for their online life.