I think your insight about Trump is mostly correct. The GOP clearly did not satisfy the demands of its base with its traditional platform of low taxes, low regulation, etc. and Trump was able to give them what they really appeared to want, which was anti-immigration policies, etc. That combined with the narrative machine of being anti-Obama/anti-democrats was a powerful combination with political polarization.
The popular vote favors urban interests precisely because way more people live there. It is the fairest way to distribute voting power; especially compared to the Electoral College, which dramatically skews it towards rural and less densely populated areas.
Swing states are not at all representative of the broader electorate. Take Wisconsin for example; its electorate is way different than other states. It is the same with Pennsylvania, Florida, etc. Why should voters in these states have such a disproportionate impact on the outcome of elections and be able to skew policy in their favor so much (research shows battleground states in elections command disproportionate shares of federal funding, policy choices, etc.)?
As an example of how distorting it is, see this recent article from Nate Cohn: https://www.nytimes.com/2019/07/19/upshot/trump-electoral-college-edge-.html?rref=collection%2Fbyline%2Fnate-cohn&action=click&contentCollection=undefined®ion=stream&module=stream_unit&version=latest&contentPlacement=2&pgtype=collection
I think what you are missing is the structural effects the Electoral College has on politician incentives and advantages for the current, extreme version of the Republican party. Reforming this would level the playing field more, drive turnout and get more people participating, and generally improve the functioning of US elections.