Not sure the lottery would earn much on interest. Rates on safe investments are very low. And funds held as cash may earn little to zero, or even below zero interest (some banks charge fees for those with very large balances). Also, unlike Ohio Lotto, which rolled for years, a PB jackpot is unlikely to rollover for more than a few months. In short, interest is peanuts compared to simply selling more tickets at near 50% markup on a large jackpot.
As for impossibility, the Mega Millions jackpot odds are 1 in ~259 million, and it's still been getting hit relatively often. Struggles to get over $200 million. So 1 in ~292 million, presumably, won't be near tough enough. For anything approaching "impossibility" based on current level of sales, 1 in a few billion odds is what it would take. Or to put it another way, the percentage of combinations sold would need to be well under 1% for each draw...
However, with random events, there are no guarantees that would be sufficient, as the Monopoly Millionaires' Club (MMC) well illustrated - it had an early top prize winner despite relatively low percentage of combinations sold.
The big flaw in the MM, and soon to come, PB jackpot odds changes is it reduces play. So while the odds of hitting a jackpot in any drawing is worse, odds of the jackpot getting hit is also a function of the number of draws. Every draw, regardless of how few tickets (other than zero) sold, is a chance of the jackpot being hit. This is what doomed MMC - too little play per drawing. The ideal situation is a lot of play combined with difficult odds. Both MM and PB (by doubling the price) have upset that balance, leading to reduced sales and less super-sized large jackpots than in the past.
Excess greed is leading to the slow demise of both MM and PB. If the situation doesn't improve within a few years, and sales continue to stagnate / lack of super-sized jackpots, it's highly likely both could be combined into one game drawn twice per week. There simply may not be enough player interest to support two national jackpot games.