Online sellers primarily will sell from individuals in another state. This is why they should not collect taxes, because they have no way of knowing what the tax rate is in each individual state. They also do not likely have the technology and manpower to collect taxes from every single buyer.
No, online sellers should not collect taxes, because it discourages online sellers. Collecting taxes is a lot of work and online sellers often do not know how to collect taxes. That there are no sales taxes online is also a big attraction for people to shop online. People know that they can save taxes, which often cancels out shipping charges.