There are a few relevant data points. While there are lots of countries that elect their Presidents by direct popular vote, Gambia to my knowledge is the only one that uses plurality elections. Every other country that does this uses the alternative vote or a run-off if no candidate gets 50% + 1. The United States if it adopted this amendment as written would still be an anomaly, in directly electing its president but not requiring a majority.
Second, the 40% rule comes from New York politics, where primaries (but not the general election) go to run-offs if no one gets 40%. New York is the only place in the world that does this. Proposals to remove the electoral college in the US always have the 40%, not the 50%, requirement because the amendment that came closest to doing this had 40%, because the amendment happened to be modeled on the New York political system.
Third, countries that elect their head of state indirectly (though there is no equivalent to the US electoral college in use anywhere), do so it the head of state is supposed to be a figurehead and the head of government is a Prime Minister. The USA is the only country with indirect election of a head of state who has real administrative power.
Fourth, there has not been one election in United States history that did not have a candidate who won at least 40% of the vote. The closest was 1860, not a good precedent, because Lincoln was not on the ballot in ten states. There have been a few elections with different popular vote and electoral college winners, and a large number of elections where no one got 50% +1. The 40% or under requirement for a runoff would effectively be a popular vote plurality system.
The main effect is that the strategy of the national campaigns would change. A second order effect that the federal government would almost be forced to introduce a non-partisan electoral office to count the votes nationwide in at least presidential elections, though I think this would be avoided for as long as possible. Again, the United States is unique in not having this.
While there have been no elections where at least one candidate won under 40% of the national popular vote, after 1970 there were two electoral college reversals (different electoral vote and popular vote winners). There have been four elections where the national popular vote margin was less than 3% (1976, 2000, 2004, and 2016, with 2000 and 2016 being reversals). In any of these four elections the second order effects on campaign strategies might have produced a different national popular vote winner. But if Carter still wins in 1976, Gore winning in 2000 probably would be the first big change.