Why is ऐ romanized as “ai” and औ as “au”?

I recently started learning Hindi, and one thing that struck me as odd was that ऐ is romanized as “ai”, and औ is romanized as “au”, even though they are pronounced /ɛː/ (like “e” in “bet” but longer) and /oː/ (approximately like “aw” in “raw”), respectively.

This seemingly breaks the logic of romanization of other vowels used in Hindi. For example, there is:

Now, ए is romanized as “ē” or “e”, so why not romanize ऐ simply as “e” with an added diacritical mark, e.g. “ê”?

This would definitely make more sense, but it turns out that the commonly used romanization exists for historical reasons. The Devanagari script had been romanized by scholars studying Sanskrit (an ancient Indic language from which Hindi developed) long before Hindi was standardized, and the two vowels were pronounced differently in Sanskrit.

In Sanskrit, ऐ is pronounced /ai/ (“ah-ee”) and औ is pronounced /au/ (“ah-oo”), so the transliteration makes perfect sense, doesn’t it?

Unfortunately for Hindi students like me, this makes romanization of Hindi a little bit more confusing, but it is not such a big deal that people would feel compelled to change the convention.