> What stops children from paying someone to buy beer and cigs for them?

I preempted this line of questioning. I'll quote the section for you:

  What you propose doesn't make stores any money, so either you have to spend a bunch of money to induce them to carry the tokens [1], or you have to have harsh penalties for "losing" shipments of tokens. If you risk harsh penalties for choosing to sell the tokens, why even bother? Stores put up with the risk of selling booze because it's *quite* profitable... selling 5c or 0c tokens absolutely is not.
  
  [1] Where does that money come from? From you and me, of course!

No business is going to risk any part of their business by selling seriously-age-restricted goods that they get essentially no profit from. In order to get a business to deal in them, either they will give zero shits about who gets the tokens (because there's no penalty for not caring), or they will get paid a lot of taxpayer money in order to make up for the state-imposed loss when they inevitably give some to under-eighteens. [0]

> The only requirement is that the sale and the process of paying for the sale isn't linked to the ticket.

Unless you make it turbo-illegal to link those pieces of information (even weakly), then those two pieces of information will be linked lickety-split. As aspenmaver mentions, lotto tickets are activated at time of sale by phoning home to -I assume- the issuer of the ticket, providing a ready-made mechanism to correlate which tickets are sold to which person. When the people who are crying to protect the under-eighteen from the "evils" of computing notice that under-eighteens are -shock! outrage!- still exposed to that "evil" despite this token-distribution scheme, they will demand any such laws be weakened or eliminated.

[0] ...or fail to strictly follow all of the regs when giving one to a "Token Commission" officer doing an undercover buy, as absolutely happens with alcohol sales...