This seems to me well explained by the standard econ concept of lock-in, where the costs of switching rise with the tenure of a relation. Before you form a relation, you want to project high switching costs, while once you are locked in, you want to project low switching costs.In many situations, customers are forced into keeping existing relationships with companies because it's too much of a hassle to switch. Cable companies can lure customers away with great introductory rates, but many will be reluctant to switch when the rates reset, as it means wasting yet another day waiting for a different cable guy to show up. A recent college graduate can be lured to a new job with a high starting salary, but once he's put down roots and enrolled his children at the local schools, it will be hard for him to leave for a different job in protest against meager annual raises.
While this certainly is not true of all of them, many online firms behave the opposite, making it extremely easy for customers to leave. You can set Gmail to automatically forward all incoming mail to another address, which requires effort from Google's servers without any chance at earning advertising revenue if you never have to log in again. If I want to ditch Blogger or WordPress, there are options to export the entire blog, including comments, elsewhere (WordPress even extols its users to "go easy on it," as the process is very "resource intensive"). However, my friend points out that your links to prior posts will no longer go to the right place, nor will links throughout the Web to your old material.
The above-mentioned products, unlike the offline examples cited in the first paragraph, are not things that you pay for, but your increased use of them results in more profit for the companies in the form of advertising or brand building. So why are they making it so easy to leave, sometimes at great expense to themselves?
The classic lock-in dynamic isn't quite the same for ad-supported online products. The cable company wants to attract you with low rates and then lock you in with high rate when you are reluctant to switch. An employer might want to attract you with a high starting salary but then offer you paltry raises when you've committed yourself to the company (noted, however, that you could retaliate by working less diligently). But for ad-supported products, I would think that an ad impression to a frequent visitor of the site would count just as much as one to a first-timer (though sites that require log-ins will be able to target the established user better and thus charge higher ad rates).
The offline examples also involve more substantial fixed costs. Recruiting, hiring, and training a new employee is costly, as is moving to a new city to take a job, so it's not in either party's interest to constantly be threatening each other and trying to renegotiate. With a free blog or an e-mail address, the stakes are lower, and Google doesn't have much incentive to hold hostage an e-mail account you're never going to check anyway (and it may even generate goodwill and your use of its other products if it makes it easy to leave).
For both online services I've mentioned, exporting all of your content can serve another purpose: backup. However, the big online players already do extensive online backups, and service outages are extremely rare, so any effort by the user is likely redundant and a waste of the server's resources.
Lastly, if some customers know early on that they will have a way out, they'll be more likely to try a new e-mail host. Yet signing up for an account takes minutes, and it's unlikely that most people would even think to research it, and the vast majority will never care.