Why don't some encyclopedias have references?
Why is this allowed and accepted?


In short, because Encyclopædia Britannica is independently published and can make its own rules. If they want to publish an encyclopedia with no references, they're free to do so. And there's clearly demand for it, since it's one of the most popular and respected encyclopedias in the world.

Since an encyclopedia is a tertiary source, there would indeed be a great deal of merit in citing its assertions, a model used by other encyclopedias (like Wikipedia). But its general audience probably care little and the publishers don't see it as worth the effort of obtaining, formatting, and maintaining reference lists that very few readers will ever use.

Britannica makes a big deal of its contributors' impressive credentials, and expects you to trust their word as experts in their fields. Since the majority of the encyclopedia's content is likely to be uncontroversial common knowledge within the relevant field—and a great deal of the knowledge therein likely predates the formal system of publication and dissemination of research in an easily citeable format—they think that's enough.

If you disagree (which is an entirely reasonable stance), read a different encyclopedia, or start your own.