Also you’re not really signing an agreement that they can fire you, you’re signing an acknowledgement of the at-will employment status so you can’t claim any illusions that you had an employment contract, but that status is typically derived from state law and advertised on the job posting you applied for. That paper you’re signing is about the same as an acknowledgement of the warning that you shouldn’t eat tide pods. It’s there because stupid people have necessitated it.
Speaking as a long time employee and now as an owner/employer, I’ve always thought people who bristle at at-will employment don’t really get it — it’s a two-way street, as an employee you can leave anytime, being considerate of professional courtesy for notice, etc.
I was always highly confident in my value and skills, so the idea of an employer randomly laying me off was never an issue - their loss more than mine. Your life will be far less stressful if you can develop that mental confidence and self-actualization, and if there is something preventing it, work on that. Specifically, if you feel lucky to have been employed in your field, and are barely hanging on to your job, maybe you should find a better field?
At-will employment should not even remotely be a big concern in life. Talent is hard to find - there’s more money than talent out there.