1. It would not be simple. You would still need means testing. You would, for example, have to prove you are of age, and not over retirement age (have you considered that?). You would have to prove you are a citizen. You would have to prove you are not otherwise employed. All of these require bureaucracy to be enforced.
2. Simply being able to declare you're unemployed and them take you at your word most certainly means MORE incentive to cheat the system, not less, because you could be working a job or jobs and attempt to collect this new welfare payment in addition to the other payments you get.
3. Removing the time limit merely opens to door for those who would stay on it permanently.
Basically, you're creating a brand new, massive welfare program that would have all the same problems and inefficiencies current welfare programs have. You seem to think people are noble and will only take these payments until they are able to work again, but at the same time you destroy your premise by stating that you want to give payments to people who have never worked and never intend to work. You want to pretend a program that temporarily helps industrious people can permanently support non-industrious people with the same efficiencies.
THAT is why your fantasy is only a fantasy.
Most of that already happens. And there are already income reporting requirements. For example, if you already make the equivalent or more than the minimum wage through passive income you could be considered self-employed. A minor would need to petition for emancipation to be considered an adult. And, there is no immigration clause in our federal Constitution. We have a naturalization clause and that means all foreign nationals in the US should be known to the general Government and federally identified for civil purposes.
EDD could receive employment information from people who are employed with an employer for simple verification purposes. Additional metadata for the general welfare should be a good thing. That process would be simpler than employers having to actually maintain individual accounts for their employees or having to litigate unemployment benefits, which also cost time and money for the employer.
Removing the time limit means we should have no one falling through the cracks and homeless since there is no time limit for capitalism's natural rate of unemployment.
There should only be time limits on our alleged wars on crime, drugs, and terror.