I'm not familiar enough with the situation in the US to comment for what's happening on your side of the ocean.
In my country, there are laws to protect both sides. Unless an agreement is negotiated, the employee cannot leave without giving a ~2 months notice, the employer cannot fire/layoff withing giving a ~2 months notice.
In many cases, though, there is a strong power imbalance. If, for some reason, you decide to sue your (former) employer, or if your (former) employer decides to sue you, you most likely cannot afford the same budget for lawyering up as they can. Also, your main power against your employer (besides possibly unions) is, as you mention, the ability to change job, but that only works when changing job is possible. Both for highly skilled positions and unskilled positions, getting a new job is hard and may require you to move to a new place - something that you may not be able to do if you have children or a working spouse.
As anecdotal examples, I know former C*Os of influential companies who have been working make up jobs for several years because they cannot find anything matching their skills, even at much reduced salaries. I know burnt out teachers who do not leave their jobs because nothing matches their skills. I have several friends in IT, or in admin positions, or with lawyer degrees who just cannot find anything or could not find anything for years because they happen to live in the wrong place and cannot leave because that would cost their spouse a job or they would abandon elders, etc.
Having myself changed (HN-style) jobs a few times, I can confirm that it's long and certainly not easy, in particular when you also need, at the same time, to care for a young child, or a sick family member, or when you're burnt out, or depressed by a personal crisis, or by the rejections you encounter from potential employers, or by the institutional bullying on unemployed people. I imagine it's even harder as you get older - I'm not looking forward to be labelled too-old-for-HN-style-jobs.
All of that is in a G7 country whose unemployment rate is decreasing. Testimonies from friends in neighbouring countries make me feel that it's even worse in many places. Testimonies from friends in the US make me feel it's not as rosy as you describe, at least not in all fields/regions.
So... yeah, I believe that there is a power imbalance. You may be in a field and/or location in which you do not witness it, and if this is your case, I'm happy for you. But for many people, it exists.