The cost of shipping is generally about the same as the cost of sales tax. It evens out for the most part (free shipping comes from somewhere as well.) There is no inherent advantage to it. By being forced to collect out of state sales tax, these out of state entities are being told to do something by a state that they have no dealings with, gain no advantage from and without compensation.
The idea that this will even the playing field for local businesses is extremely short sighted. A lot of local businesses have websites or sell through sites like eBay. They will also be impacted as will businesses that might be thinking about going online to increase their sales even if their intent is to mainly sell locally.
There is a reason that companies like WalMart and Amazon are supporting this legislation. It will kill off their competition, including local businesses, many of which depend upon online sales to boost their revenue.
If states want to continue to push their (unconstitutional...it is just a way to levy sales tax on sales outside of the state) use taxes, then they already have that avenue. There is no need to burden and in many cases kill off businesses because they don't want to go the even uglier route of pushing their use taxes.