Multiclassing is a core component of DnD, so it should be present before the end of EA. It would be feature incomplete if I do say so.
I have very little opinion on multi-classing in general; I could take it or leave it. But to call it a core component of DnD is entirely misleading. Multi-classing didn't exist in 1st edition, and in 2nd Edition AD&D it worked very differently (just play BG1 or 2 to see). It existed in 3rd/3.5, and that was the only edition where it could have been considered a "core" feature. It technically existed in 4E, but it was terrible and also we don't talk about 4E. And in 5E, while it exists in largely the same manner as it did in 3.5, it's also specifically listed as a variant rule; it's not part of the core experience by any definition.
Short version, multi-classing as it currently exists is not a core feature and its lack would not a missing feature so much as an extra idea that was not implemented.
