That's certainly not the case. The electoral college was designed such that each state's legislature chooses how to attribute their electoral college votes. Many states in the first few presidential elections just had their state legislatures assign the votes.

But still, I find it difficult to believe that the people who designed the electoral college would think it's okay that we held a national election, we got to see who wins the popular vote, and we still choose a different person for President.

As I understand it, many of the founding fathers explicitly feared that general populace would vote poorly and wanted people who were educated and had access to sufficient information to make a decision to do so on their behalf.

the rationale for it is laid out in a few paragraphs in the federalist papers number 68

https://en.wikipedia.org/wiki/Federalist_No._68

basically they wanted smart people amenable to debate and not be corrupted by a foreign nation to pick a president that doesn't have the nation's best interest at heart. or a vile person.

considering they do not do that anymore and vote based on popular vote per state it's a vestigial tail of our democracy. also, considering they were supposed to not cap the number of house of representative members and the delegates were based on this number also means that it's corrupted even more so than it was.

I was also told the following rationale: If elections are decided entirely by popular vote, then candidates are incentivized to campaign in population centers, and have no incentive to ever visit sparsely populated states. (Like, bringing your margin from 70% to 85% of 4 million people is worth more than going from 0% to 100% of 400k people.)

Except it's simply not true. Instead candidates focus on a set of fairly high-population swing states, Michigan, Wisconsin, Florida, Virginia, North Carolina, Ohio, Pennsylvania.

That only makes sense if you believe that land area is the appropriate unit to attempt to equalize political influence over, rather than people. If you think the people are who should have political influence in a democracy, rather than units of land, then it should be desirable that politicians campaign to as many people as they reasonably can.

It's not equalizing political influence between states (that is, bringing them into equality), just bringing them somewhat away from inequality. (Also, states don't have equal land area, it's more like political districts.) The electoral college gives votes as a linear combination of "per political district" and "per people", with 435/538 = 80.8% being "per people".

Also, I guess it's the fact of "winner takes all within a state" that disincentivizes candidates from simply drumming up more support within states they've already won, more so than the distribution of votes per state.

Land area is not the appropriate unit. States are the appropriate unit.

Absent the electoral college there would not be a United States of America.

The parent comment referred to sparsely populated states. That is a function of population and land area.

Have you considered the idea that what the founding fathers believed is irrelevant?

Just asking, I'm not an american.

We haven't chosen to throw away their plan. So long as we're trying to follow it, it's a good idea to understand how and why they arrived at it.

I think it is largely irrelevant, except that it can be useful to debunk people whose arguments depend on false claims about what the founding fathers believed.