I did. I think it's reasonably clear in the state tax forms that you're supposed to pay use tax, and the clean conscience was worth the $13 or whatever it was.
Obviously, though, as you say you can pay nothing without suffering any consequences.
$13 isn't a lot to pay. However, if it takes an hour to save and itemize out of state invoices, in order to pay taxes on them, I'm going to guess that's less than you make per hour, so the entire exercise represents a net loss (other than the benefit to your conscience).
Many people spend way more on out-of-state purchases, so their sales tax bill would be in the hundreds or thousands of dollars. There's real incentive not to pay, unless you're itemizing those purchases as deductions on your income tax or unless you're making the purchases as an incorporated entity.
People get audited on their income taxes all the time. Businesses get audited. I have never heard of an individual getting audited for failure to pay state use tax on out-of-state purchases when they didn't declare those purchases on any official forms.
A few states don't even have income tax; in those states there are no state tax forms that the average citizen ever encounters.
Even with 100% honest taxpayers, the use tax still puts local business at a disadvantage, due to the time value of money. I'd much rather pay later, with "worth less" dollars, than pay now.
Obviously, though, as you say you can pay nothing without suffering any consequences.