Two big points about BI:
1) You seem to be thinking of idealist communism, where everyone gets the same paycheck no matter what they do. BI is not like that. The idea with BI is that you get a basic income for nothing. It's just that: basic. Not luxurious, not even very good. Enough to live in a crappy little apartment with a roommate maybe. The incentive to do better is simple: do you want to live in a crappy apartment with roommates, or do you want something better? If you want more than the basic, then you need to get a job.
2) For the "not-so-huge wave of accomplishment", you're missing something pretty big: crime. All those lower-class people getting checks from the government may not be accomplishing much, but they're generally not committing crimes, and as a result, our crime rates are at historically low levels despite what the sensational news media would have you believe. Now why aren't they accomplishing more? Probably because most more-capable people aren't on welfare, they're gainfully employed. But you're also missing other stuff: a lot of these people getting government checks DO work, they just do it under-the-table. They do odd jobs: home repair, yard work, etc., and get paid in cash so they don't lose their check. The government may not like this, but it does add to the economy, and it shows that BI is a workable concept: these people frequently DO want to work, but for whatever reason, regular full-time employment escapes them, either because there's not enough full-time work available (and part-time doesn't pay the bills because there's no benefits and the minimum wage is too low, so they stick with welfare and under-the-table work), or because they have some physical or mental problems that keep them from holding down a regular job. Whatever the reason, most people really do want to make more money than the bare minimum, you just don't see it because it's cash-based and not reported to the IRS.