Lottery can help put money in a lot of different places. The funds can be used for social services or rebuilding. It's what the states do on the local level. The way to do a national lotto is not in my mindset though. I don't know how you can pick one winner out of the whole country.
Yes, I think that it would be a good way to make a whole lot more money for the governmetn, that they could take and maybe give to some good programs that would end up helping out a whole lot of people that need it here in the US today.
We already have some multi State lotteries that are very popular and have massive top prizes, I think the Federal Government could only stand to benefit from creating a nationwide lottery and using the proceeds to put back into the Nation through public works and education financing, overall I think it's something smart for the Government to consider doing.
The government should not get into the business of a national lottery. This always harms the most poor and vulnerable in our society. They try to buy lottery tickets that they can not afford to try to get lucky and get very rich. The poor always spend a higher portion of their income on lottery tickets.
No, I do not believe that the United States would benefit from a national lottery, because they should not be engaging in the proprietary function of running a lottery. Lottery is not part of the U.S. constitution. The states provide fair oversight to the lotteries they run. Having state lotteries also means more winners.