Might無しでも成り立ちます。
⇒Speakers of primitive languages have often been thought to exist, and there has been a great deal of speculation about where they live, and what their problems are.
ただ、そのSpeakers of primitive languagesはexistではなくて、thought to exist(存在するだろう(かも))です。
ですので、where they live(どこで住んでいるか)やwhat their problems are(問題は何か)でなくて、where they might live(どこに住んでいる(かも)なのだろうか)やwhat their problems might be(どういう問題がある(かも)のだろうか) のほうが自然です。
Mightはその「かも」「だろう」の意味をもちます。