An ecommerce website can certainly allow purchases without registration. Usually, the buyer still needs to enter most (if not all) of the same information to checkout even if they are not required to "register".
It makes more sense for a site that sells products that may not stimulate repeat business/purchases to offer non-registration checkout.
In either case it is a good idea to point out the benefits of registering.
I agree completely.
Most people don`t realize that any time they require registration, they are shooting themselves in the foot a little. So it becomes a math formula - expected loss of new customers measured against the likely hood of a return customer.
So if you are selling books or prescription medication`s, registration is good. If you are selling caskets or coffins though, you are shooting yourself in the foot.