It's a fair question, and I had to think about it.
I think what it is is that even though it's an Arcane spell, it's "granted" by the Patron. And that Patron can be almost any sort of being...Fey, Celestial, Abyssal, Undead, Draconic, etc.
And it's true that the Warlock's other spells are also granted by their Patron, and many of those are on the Wizard lists but not the Cleric list, so the same question could be asked of those.
But not only is Eldritch Blast exclusively a Warlock thing, but it's also:
a) Just a cantrip
b) Just an attack cantrip, of which everybody has at least one
So basically there's nothing in the fiction that, to me, makes sense as to why every single Warlock, regardless of Patron, gets this spell, and nobody else does (except for the Bard edge case). It just reeks of the designers saying, "Let's give this class a really cool attack cantrip that makes them special" with zero fictional support.