EMD's will not rank alone without lots of support
This has not been my experience at all. I have no problem getting EMD domains to rank still. Yes... the days of buying an EMD, throwing up a 5 page WP affiliate site, and submitting to 10 free directories to get to #1 are over. But an EMD with quality content and a couple dozen quality links can still catapult to #1 even for competitive phrases. The key IMO is quality of links and content.
I find it just as easy to get quality links for EMD sites as any other types of domains. In fact, because they are more niche than a single site trying to rank for many things, EMD domains are often easier to acquire quality links.
The key to getting high quality links is having great content, a great resource of some type, and/or great tools... This makes building links exponentially easier. No authoritative, quality site is going to link to a low quality or even mediocre site. Doing so reflects badly on their site to their visitors.
If you're having problems building links for an EMD domain (or any domain for that matter), I would take a long, honest look at what you're offering on your site as far as content that would/should make another webmaster want to give you an editorial link. I bet that 99% of the time, having low quality or mediocre content that can be found on thousands of other sites on the web is what makes acquiring high quality, editorial links from authoritative sites hard.
If you have GREAT content and are still having issues then you're likely either going after the wrong kinds of placements or your phone script, email, or whatever you're using to contact other webmasters... is likely impersonal and could use some work.