And this is why the model would not work. I don't believe that there are enough people who would find fulfillment in flipping burgers, unclogging toilets, roofing in AZ in July...
I think you missed the "worth it" part, which substitutes for the "fulfilling" part. Unattractive but low-skill jobs would see higher wages (and, thus, greater incentives to find labor-saving alternatives) until the utility people doing those jobs provided to others was reflected in the reward people doing those jobs received.
The jobs' salaries match what they are actually worth, and can't be offered as minimum-wage jobs that people take because they don't have any money and can't get a job elsewhere.
Which means burgers will cost much more than they currently do.
The same will be true for all domestic products/services where a significant part of the work force currently has low wages.
Which means that you and I will pay more for goods/services than previously. The effect will be similar to a significant sales tax, might as well try funding BI that way (at least imported goods will carry some of the tax burden) and look at published studies on the effects of sales taxes...
Don't worry, the hedonistic urge is stronger than laziness in most people. Especially since lazy usually implies watching TV which continuously bombards you with advertisements to buy things...