Most EVs do have such a speaker. But it only plays when they're driving at low speeds where they could be a threat to pedestrians, bikes, etc. And also there's no standardization of the noise.
All EVs have a speaker and the noise is standardized. The problem is there is a different standard in each country and the solution is to make one noise which covers all of the standards - thats why it ends up sounding so strange. The combination of the various standards varies from OEM to OEM - thats why it ends up sounding different OEM to OEM.
I mean... maybe in the US? Here in Canada all the EVs seem to make a different noise. The noise my Volt makes is entirely different from my friend's 2nd gen Leaf, for example.
Maybe that's changing with the latest round of vehicles, but I don't recall hearing about any regulation passed.