In this article Barry Abel lays out the benefits of email over direct mail. Here are some of his arguments:
E-mail costs: For companies whose customers are largely online, e-mail is a cost-effective replacement to direct mail. For organizations that have a blend of online and non-online customers, it can be a welcomed alternative for e-mail-equipped recipients that also lowers the cost of marketing for the company.
Direct mail efficiency: A direct mail campaign can take weeks to design, lay out, print and mail. Moreover, while deliverability and response are trackable with direct mail, they take time. Undeliverable mail can take weeks to be returned and addresses must be manually removed from a list. In addition, response can take days by postage paid reply.
E-mail efficiency: An e-mail campaign can take as little as a few hours to a few days from concept to receipt, enabling companies to respond rapidly to market dynamics and competitive pressures. In addition, with e-mail sent by an advanced e-mail delivery system, bad addresses are discovered within minutes and culled from a list. Then, marketers know exactly how many recipients opened the message.
I don’t think you should entirely replace direct mail with email, both channels have their place in the marketing mix. Smart marketers use direct mail for their higher value customers/segments and add the email channel to their communication mix to strenghten the offline channel.
For segments where direct mail is not very ROI positive, I would definitely recommend increasing the use of email marketing and reducing direct mail – because due to it’s cost-effectiveness you’ll be able to reach out to a larger target audience, while still being able to segment and target this audience with different messages.
Would love to hear your view on this!
Be Relevant 
One of our clients is a direct mail company so I know a bit the industry. While it is true that email marketing is far cheaper than direct mailing, the possibilities to think “out of the box” are a bit limited. Say for example you want to send your customers, next to an invitation to an event, a cool gadget: this is for sure not possible with email.
I agree. But even in this case it makes sense to combine email with direct mail. eg. announce the cool gadget in an email a couple of days before the direct mail piece arrives, so that the recipient will expect it. Or follow up the snail mail event invitation with an email reminding people about the event. The opportunities to integrate both channels are endless.