But why would "emotionally driven" people be interested in EA? It doesn't offer them the required emotional appeal (note: I'm talking about EA activities, not EA marketing). If the marketing promises them rescuing cute puppies in distress, EA won't be able to deliver.

Well, it depends on what you're advertising. If you're advertising deworming you talk about the suffering of children in these countries and you show some heartbreaking images (I'm being deliberately vague here, but you get the idea.

If you're advertising animal welfare, then yes, you can show cute puppies.

Besides, are you quite sure you want to compete on the emotional-appeal basis? You become a very small fish in a big pond with some pretty large megalodons swimming around.

You wouldn't consider "people who are emotionally driven" as a target market. That's far too big a market for a small movement like EA (probably containing somewhere between 40%-95% of the global population). Instead, you would start out with a smaller market that you expect contains many emotionally driven people. You move to the bigger ponds once you have the capital to compete in them.