I've had a "we own everything you make" clause in contracts before, it's just copy pasted boilerplate, and they were fine with removing it when I asked.
Noncompetes I've been fine with, because they were always quite niche companies, and the wording was something along the lines of "don't join our direct competitors for a few years", and that seems ok to me. I will grant that it gets more complicated with megacorporations that work on everything though, as their "competitors" are roughly everyone.
A number of years back, our company was acquired and they sent us employment contracts from our new owners, with that same "sign it or GTFO" message. Many people signed. A few of us just didn't. Nastygrams kept on coming, we kept on ignoring them. Ultimately, we never did end up signing.
Which is the other piece of the puzzle - lawyers are really good at knowing when they actually have power and when they do not. Unfortunately, when they don't truly have legal power they resort to bullying. So if you are being bullied to sign a contract, that usually is a red flag to stop, really look at things, and figure out why they are using that tactic. You may be in a better situation than you think.
I think you might be a bit presumptuous. Why do you believe they don't have legal power? If you are an at-will employee, you can typically be fired for any reason. Not signing the updated employment agreement is, unfortunately, a valid reason.
In your case, they did not exercise that right. But I've been at places where they did. For something as petty as not signing an agreement which appeared to eliminate some employee benefits that were contractually obligated. Could the fired employees have sued, and won? Perhaps. But it would be an expensive, risky, time-consuming proposition to find out.
Noncompetes I've been fine with, because they were always quite niche companies, and the wording was something along the lines of "don't join our direct competitors for a few years", and that seems ok to me. I will grant that it gets more complicated with megacorporations that work on everything though, as their "competitors" are roughly everyone.