eCommerce orders table. Save prices, or use an audit/history table?
As you've identified, storing the price on the order makes the technical implementation easier. There are a number of business reasons why this may be beneficial though.

In addition to web transactions, many businesses support sales through other channels, e.g.:


Over the phone
Sales agents "on the road"
At a physical location (e.g. shop, office)


In these cases the order may be entered into the system at some time after the transaction took place. In these circumstances it can be difficult to impossible to correctly identify which historical price record should be used - storing the unit price directly on the order is the only feasible option. 

Multiple channels often bring another challenge - different prices for the same product.  Surcharges for phone orders are common - and some customers may negotiate themselves a discount. You may be able to represent all possible prices for all channels in your product schema, but incorporating this into your order tables can become (very) complex. 

Anywhere that negotiation is allowed it becomes very difficult to link price history to the order price agreed (unlesss agents have very narrow negotiation limits). You need to store the price on the order itself.

Even if you only support web transactions and having a relatively simple pricing structure, there's still an interesting problem to overcome - how should price increases be handled for in flight transactions? Does the business insist that the customer must pay increases or do they honour the original price (when the product was added to the basket)? If it's the latter it the technical implementation is complicated - you need to find a way to ensure you're maintaining the price version in the session correctly.

Finally, many businesses are starting to use highly dynamic pricing. There may not be one fixed price for a given product - it is always calculated at runtime based on factors such as time of day, demand for the product and so on. In these cases the price may not be stored against the product in the first place!