For demons particularly the Lords of Hell, the less they speak, the less human they feel. Demons are inhuman and otherworldly creatures of pure evil, a person can't reasonably expect to understand that and retain their sanity. In fact, according to Diablo lore, the D2 heroes went mad from their experiences, yet we really don't get that vibe much in D3. Historically Diablo has had very little to say until D3, the only one I can think of is his one liner from the battle with him in D2, I don't think he said anything in Diablo. Moreover, the atmosphere and his actions alone tell the story without him having to utter a word.
Same thing applies to D3, if they simply cut off all but a few words for the Diamond Gates cinematic and when you reach him at the Crystal Arch, the visuals alone give you a good enough sense of what is happening. Alongside the imagery in the cinematic and what the Angiris Council has to say along the way, that is sufficient, his talking just kind of kills the inhuman aspect. The dialogue during the phases of the battle are also lackluster and are better off not being said especially given this running joke: "TERROAR!"
I laught every time i hear Diablo scream "TerroaRRRR"
Yeah great TERROR for Diablo fighting a full equipped Monk.