Because although you can, you won't - probably because there's not 'news' every week about a billionaire randomly giving a person half his fortune. The lottery win happens to somebody, while the billionaire scenario doesn't.
If someone established a reality TV version of something like The Millionaire [http://en.wikipedia.org/wiki/The_Millionaire_(TV_series)] then I bet people would start having that sort of daydream. Perhaps such a show would even lead to a decline in lottery ticket purchases, since the get-rich daydream would be available from another source.
I think an important piece missing is the active vs passive decision making. When you purchase a ticket your are actively triggering the thought process.
In your scenario there would be a passive trigger that would dull the entertainment affect.
I wouldn't discount the little piece of paper with numbers on it.
My buddy Bob dreams and doesn't buy a ticket. His rationale: his chances of the winning ticket blowing down the street and into his open hand are microscopically different from his chance of buying the winning ticket.
Honestly, that could be it. Signalling isn't always about showing off -- many times it's just about signalling a willingness to belong. Even signalling a willingness to belong to an objectively undesirable group.
So it could be signalling that you're not "puttin on airs" by acting superior to those around you who play. Or it could be signalling that you legitimately like to belong to the group around you who play. Or it could be simply signalling that you don't take yourself (or $2) that seriously.
If someone established a reality TV version of something like The Millionaire [http://en.wikipedia.org/wiki/The_Millionaire_(TV_series)] then I bet people would start having that sort of daydream. Perhaps such a show would even lead to a decline in lottery ticket purchases, since the get-rich daydream would be available from another source.