There are major problems with not having a drawing for a typical jackpot game until every single combination has been sold. The main one is how difficult it would be to sell all of the combinations. The frenzy over raffles is produced by the perception that the odds are better and the fear of not getting a ticket while they're available, and that won't exist for the game you suggest.
I can promise you that plenty of people play 1 2 3 4 5 6 for every drawing (I had a coworker who was one of them), just like plenty of people play diagonal patterns. Those "seasoned lotto players" don't play it because they think it's too unlikely to be drawn. Other people play it is because they think nobody else would choose it and/or they think it's a special number that is more likely to be drawn. Both groups are wrong.
The combinations that wouldn't sell would be the ones that nobody plays simply because of probability. As a group, people don't pick combinations randomly, but to simplify things let's imagine that perfectly random QP's were the only choice. Let's also pretend that the first 90% of combinations are sold with out a single repeat. At that point, 9 of every 10 tickets sold can be expected to be repeats of a combination that has already been played. For MM that means you'd have to sell roughly 175 million tickets to cover most of the 17.5 million remaining combinations. When 99% of the combinations were sold it would take another 175 million tickets to get most of the 1.75 million that still hadn' been played. Sell those and you might have covered 99.9%, and you'd need to sell another 175 million to cover most of the 175 thousand that were still left. In the real world it's unlikely that all of the combinations would be sold without selling at least 10 times as many tickets as there are combinations.
For the $370 million advertised MM jackpot in March they sold about 212 million tickets. To have a realistic chance of selling all combinations they would have to sell more than 5 times as many tickets. Who's going to buy over a billion tickets? How many of the people who didn't play will decide to play if the advertised jackpot is $1 billion? Would you buy 4 or 5 times as many tickets? That's the biggest problem of all. I don't think there's a chance that they could sell enough tickets to use all of the combinations.
Since people don't play randomly in the real world, some combinations would be played more often than random chance would allow. At the same time, the random combinations would start repeating when less than 1% of combinations have been played. By the time all of the combinations had been played at least once some of them would have been played 100 times or more (ignoring the relatively few combinations that are always played by large numbers of people). The good news is that the jackpot would be truly huge. It's unlikely that it would be less than $500 million cash for MM , and a very good chance it would be $700 or more. The bad news is that there would be only one single combination that could be an only winner. The most likely outcomes of the drawing would split the jackpot between multiple winners, resulting in actual prizes that are no bigger than what we see as a matter of routine. For a few combinations the actual prize could be smaller than the 2nd place prize.
If such a game did exist I'd have to assume that the average number of repeats for any given combination would be about 10, so for an advertised jackpot of even $1 billion I'd be expecting the winners to each get perhpas $50 million cash, with a fair chance that it would be less than half that much. For a $20 to $50 million cash jackpot in MM I'll spend a buck or two. That means you're going to need to break into your piggy bank to buy all those other tickets that have to be sold.