I use Camino on my mac for just this. It has the handy "porn reset" which dumps the whole session cookies and all. This is great for webdev site testing, online banking, etc.
I would imagine that by now some sites are relying more on Persistent Identification Elements more than cookies simply because fewer folks know about them, but I've no data.
Private browsing still lets your browser show cookies that it already has, it won't store new ones (except it doesn't have control over plugins, so they might).
What that means is if you are a regular Amazon user then decide to pop in as a stranger by turning on private browsing, Amazon will still know you.
What Private Browsing does do, is on window close get rid of all the cookies, history, field autofills, and such that you accumulated in two hour private browsing session searching for an opened, boxed, Luke Skywalker figure for your girlfriend. It doesn't stop the web sites from keeping track, for instance eBay might still show them in the recent items if you were logged in.
Much commerce depends on offering different deals to different sets of customers, to extract the highest price from each individual instead of relying on the "market price".
Airline tickets are a good example.
In such markets, there may be an advantage to consumers banding together to aggregate pricing information. If all users of priceline style "reverse auction" or whatever they call it shared bid info, it would turn it into a "treasurys style" auction where everyone got the best price that gave the seller the required volume of sales.
Another way to break the attempted segmentation of a market is to make the product fungible, so that a secondary market develops if there is any inefficiencies in the first market. It used to be common to re-sell unused airline tickets via newspaper classified ads, and airlines got rid of that after Flight 800 blew up (because of electrical failure) on anti-terrorism grounds. You can get back the exchangability of airline tickets through some tricks, and sell and buy airline miles on sites like points.com and flyhub.com, but that must account for a miniscule part of the market.
Back to deleting your cookies to compare amazon and hotel offerings -- wouldn't a firefox plugin that showed you what prices other people were seeing for rooms or books or whatever, when you browsed to that page, be pretty useful ? Maybe it could be monetized by commission or referral fees of some sort ?
No need to delete cookies. Whether you're on Windows, Linux or OS X... just create a new user account for the particular purchase you are interested in. When you use the browser from that account it will have no cookies. When you've finished, delete the account. Next time you want to opt-out of their 'previous customer' pricing, just create a new account.
I have FF and 1 other browser installed on each of my computers, and use each browser for different activities. But I see no need to delete cookies (and lose potentially useful information), when I can just create another user and use fast-user switching to go to that account. And certainly if someone only has a single browser installed, then I think creating a new user is probably easier than locating a new browser & installing it :-)