I've been doing an increasing number of intro calls over the past year, often with slightly younger or less well-connected EAs. 

At first I expected most of the value to come from establishing a relationship and offering useful information/advice/resources. 

Over time, however, I've found that a surprising amount (maybe most?) of the value of intro calls seems to come from vetting people, understanding their skills/abilities/general competence/situation/needs and then connecting promising people with others who can help them more than I can. 

As EA grows, coordination problems are likely to increase. And as you get more senior/established, you'll probably find yourself doing more intro calls. 

Some advice for these calls:

• Ask questions: Aim to get a good picture of the other person's strengths, constraints, and goals. This helps you make intros that are maximally useful, and also ensure that an intro is worthwhile (see fourth bullet on the costs of intros).
• Leave time toward the end of the call to explicitly brainstorm further introductions you can make. This allows you to get immediate feedback on the intros you might want to make. It also allows you to commit explicitly to making introductions, which increases the chances you'll actually follow up (see next bullet). 
• Make sure you actually follow up on any intros you said you'd make. I find sending intro emails pretty annoying, and it's easy to forget to follow up. Try to send intro emails right after the call if possible.
• Consider the costs of making an introduction. An intro call will often take 30 minutes to an hour, plus some time before and after for prep and follow-up. These calls can add up quickly, especially for more senior/established EAs (whose opportunity costs are also the highest). It's often best to ask permission to make an intro if you have any uncertainty about whether the intro will be welcome.