Taking a low paying job can hurt future earnings, but generally I agree with you. I was once reviving enough unemployment that many full time jobs would have been a payout, at the same time unemployment was not even enough money to pay rent. However, taking a job to slow the bleeding would have been more appealing.
Yep. That is essentially the crux of it and also why there's a big trade off between unemployment vs a small basic income. With unemployment you collect while having free time and then lose that income stream as soon as you take the job, making the decision to take a job significantly less obvious. With a small (survival level) basic income, having a job means you make more money...period.
It's an aspect of the equation that nobody wants to talk about. In low cost of living areas you almost have an incentive to collect unemployment for stretches because of it.