Phew!
There's several important points about Unemployment insurance that posters either aren't acknowledging or are only briefly circling around. The premise of the OP is that high levels of UI discourage working, a frequent criticism of recent UI assistance. To that end, there is already a great deal of conditions on UI specifically to reduce just such a situation
1) You must continue to search for work. While some states have temporarily suspended job-search verification, all require that you are available and able to work should an opportunity come along. WHile each state is different, the basic procedure is that every week you must certify that you are able to work, looking for work, and have not turned down any opportunities. Many states will forward job offers in your field which you are then required to pursue or risk losing your benefits.
2) If your previous employer offers to re-hire you, you must take the job or lose your unemployment benefits. A person cannot simply choose to not go back to work. Companies are contacted by the unemployment office about layoffs and re-staffing.
3) Unemployment benefits end.. Most states limit unemployment to 26 weeks. Some offer an additional 13 weeks of lesser payments. A few offer even less (e.g. Florida at 12 + 6 weeks). Additional conditions apply as well, including the maximum amount of UI one can recieve per calendar year.
4) Generally, state unemployment benefits are tied to previous income, up to a cap. This often gets overlooked when someone claims the minimum salary one needs to earn to 'get more than on unemployment'. In most states, a person earning minimum-wage and working 32 hours/week (techincally considered "full time") will not qualify for the maximum amount of benefits. In my own state it's your average quarterly earnings divided by 22 up to $420. Many other states are far less generous, a few moreso.
5) Unemployment does not consider nor include health/retirement benefits. This too is frequently overlooked. Consider a union worker earning $45k gross with full benefits. With the additional $600/wk Federal UI + state UI his/her take home pay may have been slightly less, but this person's family is now without health insurance, is not getting a company match or contributing to their pension, etc. Speaking from my own experience my employer's contribution for health insurance + retirement for my 3 person family with no underlying conditions is over $14k/year. Bottom line is a job with benefits is far more appealing than staying on UI for most people.
All of the above are conditions that most (if not all) States impose to reduce the chances that individuals stay on unemployment instead of going back to wokr if they are able. Depending on your personal ideology you can be thankful or bitter towards the GOP for pushing through most of those work requirements. In some states a few of these have been put on hold during the pandemic, but all are slated to return.
In addition there's a number of other factors which limit people staying on umployment longer than necessary
i) we stigmatize unemployment in the US.
ii) many people genuinely prefer to work. This is probably related to the stigma we attach to unemployment and the emphasis we place on being a 'productive member of society'. Work also provides other social benefits and longer-term financial security (see "unemployment benefits end", above).
iii) long-term unemployment hurts advancement and lifetime earning potential. Most people realize the longer they are out of their field the harder it is to get the job they want. Even a job that pays less has the potential to lead to a better paying, permanent position.
iv) States don't want their citizens on UI. It costs them money, they lose tax revenue, and it lowers their productivity. Through a combination of the above and various work/retraining programs they actively push people to get jobs.