In all of the economic crises of the last over half decade now, a major component of the problem has been that government revenue from taxes has continuously fallen, and that government's ability to provide services has likewise declined. Given all that, it's surprising, then, that no one has publicly raised this issue before: that online retailers have been getting away with murder, so to speak, by avoiding making consumers pay this tax, and state and local governments have been missing out on huge amounts of revenue.
There is really no difference between online stores and stores that operate at a fixed location. In fact, many stores do both. The reason there are online stores that don't pay the same taxes is that it is hard to decide which state's taxes they should be paying. However, there's no reason for them to be exempted.
Online sales has a competitive advantage by not charging and submitting taxes. While you can make the argument that the tax regime isn't fair for anyone, it still must be applied equally. If you don't like the taxes you pay, move somewhere else or vote for someone else. When sales tax is part of our economy, it has to be applied equally for everyone.
No, I do not think that any companies should be collecting any kinds of sorts of tax like this. There is the reason that so many humans on this earth are having trouble making ends meat is because places over price and over charge of everything. It is not fair anymore that we make so little for everything to be so expensive.