If I wanted to come into compliance here, I'd have to save all of my reciepts from every time I shop online, and probably hire an accountant to figure out all the extra tax I owe. This doesn't sound interesting to me, or enforceable by the government. However, online stores collecting this for me could be a value add in some ways.
Let's take a look at the free market though (although I get that issues of tax law cannot be fully free as they start in a non-free place). What if online retailers _offered_ to collect the tax for me, with the note that you owe it either way and they're trusting you to pay it on your own otherwise? I would likely opt-in much more often. Similar to suggested tips increasing tipping in NYC cabs, this might move the needle in the right direction.