e sounds more like `eh` though (at least in latin-derived languages and japanese). Pronouncing it `ay` is generally seen as a strong english accent.
`eh` and `ay` can both easily be read as a dipthong that would be represented as `ei` in any reasonably spelled language (like Finnish).
I think t-eh-n is pretty illustrative of why eh works better than "ay" either way - ay is much much closer to ey and so ei.
In some languages it's /ɛ/ (English "eh"), in others it's /e/ (Scottish English "ay"), and in yet others it's /e̞/ (halfway between the two). It's rarely /ɛɪ/ ("ay" in most dialects of English), though it appears in many other languages written as something other than "e".
Dutch is an interesting case: /ɛ/, /e/, and /ɛɪ/ are all different phonemes (short "e", long "e"/"ee", and "ei"/"ij" respectively).
Many only have one. Greek just has /ɛ/. Japanese just has /e̞/.