In some settings you don't even need to step into the Underdark. Mindflayers, Drows and other things will attack and raid the surface...
See, this exposes the flaw in your logic. If you are saying there CAN'T be safe parts of the Underdark because it's full of liches, minotaurs and Drow slavers, then by extension the same is true of the Overworld because those things come out of the Underdark to the surface. If that's the case, why can't adventurers, treasure hunters, paladins etc venture into parts of the Underdark to make them safer? Say the Flaming Fist traced Drow slaver incursions down to a surface cave outside the Basilisk Gate. Do you not think they'd maybe send forces into the cave to bar passage and maybe create a base camp in the upper levels? And if your response to that is "No it's not possible" then you haven't paid any attention to what DnD actually IS...
