I think there already is a New Improved Lottery that is played by many—it’s called drug addiction. Heroin addicts spend repeated minutes for their repeated fantasies. And their behavior at work or shopping is actually not that different from what you describe.
However, for us non drug-addled folks, there is a problem with sustained repeatable fantasy—it doesn’t exist. Buying one lottery ticket gets me one minute of fantasy, but buying 9 more tickets does not get me nine more minutes of fantasy, even if they are from different drawings. Lots of people dream about winning the lottery—how many people dream about winning the lottery twice?