Not only that, but if the election is close, the entire country gets re-counted.
The quickest way to fix the electoral college is not to fix it at all, but to increase the size of Congress. Congress used to increase in size every year, until the 1920s, when they couldn't decide on how many seats to add. In 1920, there were about 250k people in an average district. Now there are over 750k, which is larger than some of the smallest states.
Congress sets its own size, and this fix can be done without any amendment.
This doesn't really fix anything other than the small state counting bias. You still have states that are entirely ignored because they're reliably >50% red/blue and you still have a small number of close states that are the only ones who matter. There's still a high likelihood that you'll have presidents elected who lost the popular vote merely because of inefficient arrangements of voters.
No, that won't be solved without a constitutional amendment, though. Increasing the size of Congress can help mitigate the issue, and just takes an act of Congress .
That's the entire purpose of the Senate. It is functioning as designed and that is not an issue.
Congress is supposed to be two halves, one where every State is on equal footing (Senate), and one half where a larger population gets a larger voice (House).