I had to check when I lived in New York whether or not I was paying sales tax last time this came up. I was and I didn't even know. If the average customer doesn't even notice, there is no compelling reason to condone tax avoidance. It simply doesn't alter incentives in the real world, whatever ideology says.
And for the record, I do notice unexpected shipping charges when something comes from a third party vendor and I wasn't expecting this. This is a large enough difference to alter behavior. Sales tax rates in the US are simply too low to do this, even in New York. Also, Amazon has enough advantages as it is. I doubt there is a single person in the US that buys from Amazon due to tax avoidance rather than its other benefits. Well, I'll walk that back a bit. There may be one or two anti-tax extremists that use this as a reason to buy, but this is the exception. The sales tax is just too low and incidental to impact my consumption decisions in the slightest.