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There seems to be lots of discussion about why oh why do we have an Electoral College in the U.S.A. However, given the fact that we do have an Electoral College, the really seemingly odd thing, IMHO, is that all 50 states have a more-or-less similar institution that essentially relinquishes the state legislature's power by attempting to emulate a popular election. Article 2, Section 1, Clause 2 of the constitution says:

Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress…

This seems to permit a great amount of leeway to the legislatures of the various states to figure out all manner of interesting ways to appoint electors. Yet, every single state holds a popular vote for the choice of electors. To be sure, the rules vary slightly, but the electors could, for example, be voted on by the legislature during session, or chosen out of a hat or…?

I would have imagined that having been given the power to choose the electors, the state legislatures would guard this privilege fiercely, and yet they seem to just hand it to the people for no obvious reason.

For what reasons (legal, political, cultural, societal, psychological, historical or whatever) do the states all choose their electors via a popular voting mechanism?

* This question seems to be somewhat similar, but has elicited answers mostly be along the lines of “because that's how states have decided to do it.” My question is about why states have decided to do it that way.