Be careful whereof you pontificate. Different states have different laws.
In California, what you said is largely correct. The seller is responsible for remitting the sales tax to the state, whether it was collected from the purchaser or not. In fact, if the seller collects less than is due, the seller must remit the full amount due; if the seller collects more than the amount due, the seller must remit the entire amount collected (i.e. can not keep any overcharged tax).
In Pennsylvania, and perhaps other states, it is specifically ILLEGAL for the seller to include the sales tax amount in the retail price. The seller is legally REQUIRED to collect the sales tax as a separate amount from the purchaser. Or at least this was true a few years ago when my company was selling at a conference in Pennsylvania; it may not be true today, but the law was made quite clear to sellers at the event.
This is just a tiny, tiny hint of the complexity of the sales tax situation nationally. Also consider that a specific food item may be taxable in some states and not in others. Indeed, that same food item might be taxable in some jurisdictions (city, county) within a state, and not in others within that same state.
And then get into whether the purchaser is exempt from sales tax or not. For example, in many states, schools do not pay sales tax. In others, they do. It gets very interesting when a teacher goes to a professional conference in another state, and will not be reimbursed for any amount charged for sales tax even though the sale is not exempt in the state where it took place.