I think the essential problem with convenience is this: -- If you make X more convenient, you expect to have the same amount of X for smaller costs. What often happens is that when X becomes cheaper, people will use much more of X. At the end of day, your costs of one X have decreased, but your costs of total X may have increased.
For example it is more convenient to send an e-mail, than to write a postcard or a paper letter. Problem is, people will start to send many trivial e-mails with jokes etc. After a few decades many people spend more time maintaining their mailboxes than they previously spent writing and sending paper letters. Sure, we also get a lot of useful information this way, so perhaps it is a net benefit, but you have to be careful about things you did not have to be careful before.
One part of this problem may be shifting the burden of communication. If someone writes a paper letter, the writer pays the costs of communication (literally, and also in time and work), so the writer will think whether it's worth doing. In e-mail the costs are shared; and if someone sends an e-mail to a group of people, then the total (time) costs of reading that e-mail are larger than costs of writing it.
Another part is that some things are easier to automate than others. Generating noise is easier than filtering noise. Sending e-mails is easy, writing spam filters is difficult, but I would need something even better than a spam filter... something that would separate important e-mails from nonimportant, and show me only what I need and when I need it.
Gmail has a 'priority inbox' that tries to do that. I've been using it several months now, and I rather like it.
Distraction is a Symptom of a Deeper Problem: The Convenience Principle and the Destruction of American Productivity is a good article on distractions versus getting things done. With extra emphasis on how many of our distractions are the result of a desire for convenience rather than something more substantial.