I think the question should really be: what do you gain by having an Opportunity related to an Account?
The main (business) answer to that is you get a historical view of your customer that helps you understand them and therefore sell to them within that context.
By having an Account (Person Account or Business Account), you can run reports that show you all your customers that have had more than one Opportunity with you, or when reviewing a customer, you can see what they've attempted to purchase from you in the past. You can also see other interactions with them such as Cases, Activities (emails/meetings/calls), or whatever else may be important.
To me, the implication of not having an Account is that you have no context for your Opportunity. There's no way to see whether you've dealt with this customer in the past, and if you have, what were those dealings like?
Other technical things to think about:
Accounts can store the address (along with maps) of the customer.
Salesforce1 and most salesforce apps are built assuming your customers are loaded as Accounts/Contacts and therefore those tools won't help you. i.e. You won't be able to show on a map the location of your customers.
All comms (such as campaigns and a lot of emails) are usually sent to Leads/Contacts/PersonAccounts, not Opportunities.