1. This doesn't happen for the vast majority of sites, which charge the appropriate sales tax rate based on the shipping address location. Amazon individual sellers are inconsistent, but every major retailer handles it well within the bounds of the law. The issue came about partly because it was and is still often believed that one isn't obligated to pay sales tax if the shipper/seller isn't located in the same state, though the legality of this varies at best. Regardless, this isn't the "tax system" but rather the negligence of Amazon.

2. In the country where I currently live, if I order something from another country I am charged the tax on import plus a substantial processing fee that's usually much larger than the tax. I miss the US system in comparison...

It's because each of the 50 states administrates its own sales tax (or lack thereof).

Yes, but some cities and counties also have their own sales taxes, though this isn't why sellers don't charge sales taxes.

They don't charge them because they can get away with (or believe it is legal to) not charge sales tax for customers not in the state or area from which they operate.

It was until very recently.

Honestly, this is the first instance I've ever heard of anyone going to the lengths of recalling their purchase history to backpay sales tax.

If it makes one feel better to do it, by all means do it. Among the list of egregious tax offenses that exist, this is likely pretty low on the IRS list to audit people.

The IRS doesn't care about this. It's a state thing.

It only takes about 5 minutes, so it's not too onerous.

It's crazy, but states and cities need to get money somehow.

It is. It’s really annoying.

Localism is a good thing. The benefits outweigh the costs here.