Okay, currently in NC businesses which sell directly to NC residents collect sales tax, but NC businesses which sell to NC residents via Amazon don't. Whether or not you agree with NC's proposal, there are more factors here which I don't think you've considered.
the founders of this great nation realized that smuggling was a good thing
To the contrary, the United States was set up as a nation of laws and with the assumption that there would be taxes. There's nothing that excuses smugglers from the legal system.
But there is no reason why the governments should have license to grow when its supporting economy just dropped 20%.
Firstly, the proposed change in no way "grows" the government. It is simply an additional revenue stream. Secondly, since as you say the economy has dropped 20%, that means that NC is collecting about 20% less revenue. I highly doubt that this proposal will even come close to making up for this, so in total NC's revenue will be shrinking, not growing.
To argue otherwise is to argue that you can tax a nation into prosperity, or that you can lift yourself up by your boot straps.
Actually, there are good reasons why you want to do this.
First of all, the state's expenditures naturally increase during a recession. Why? Firstly, the basic costs of maintaining infrastructure do not decrease drastically: potholes in highways still need to be fixed, electric poles which fall during a storm need to be repaired, etc.
Secondly, consider that the 20% drop in the economy is not applied evenly. This year nearly 50% of college graduates didn't manage to find jobs. That is a lot of talent that is being wasted. Also, for example, some friends of mine used to be a two-income family until, in one week, one was laid off and the other had a 30% pay cut. That's a family that is now trying to live on one-third of their usual income, but their mortgage payments aren't any lower. As a result there is a lot of capable people who suddenly find themselves in deep financial trouble, if not homeless.
Because of this, the state's unemployment insurance program, its support for working families who aren't able to afford enough food for their children, homeless shelters, etc experience a large increase in the number of applicants. So, the costs of these programs rise, at the exact time that revenue falls.
What is the state to do? Not only would it be immoral to let people starve to death, it is foolish: dead people will never get jobs and help the economy in the future. You want all these talented people to be earning money, not dying in a tent city.
Instead, you DO want to have new government programs to help the economy. Take some of those unemployed civil engineering graduates and have them design better infrastructure for the cities, and then hire other unemployed people to build it. Not only do you get to enjoy the benefits in the future, but the newly employed people then spend their pay at local shops and stores, which means that those businesses have more sales, which means that they no longer have to lay people off or go bankrupt. This will improve the economy, and once it has recovered any loans that had to be made can be paid off. This just makes sense, and has worked before.