I’m not so sure this would work to the Right’s disadvantage. We start every election with the electoral votes of California and New York pretty much lost. There are a LOT of Republicans in Orange County, the Central Valley, and upstate New York. This would give them a real voice in the election. Much easier for the Republicans to pick up votes here than it is for the Dems to scratch up votes from two dozen scattered, heterogeneous, reliably red states.
I'm not sure it would necessarily give anyone a particular advantage. In almost 240 years, we've only had a person win the popular vote (allegedly) and lose the Electoral College vote. That's not necessarily why I'm so opposed to it.
I think the Constitution matters. If these people want the national vote to be the controlling (and sole) vote to elect presidents, then let them do it the way the Constitution was intended to be amended and not this clearly extra-constitutional circus that they're attempting.
Lastly, and more to your direct point, I do think that this would lead to even more corruption and ballot box stuffing in the larger cities, than even we see now. With the exception of TX, the states with the biggest cities almost always vote Democrat - NY, CA, IL, MA. The union thugs are strongest in these cities, and as you might expect, election fraud is worst in these cities. If this was enacted, I think it's possible that you would see more votes cast in those cities, than there are people who actually live there. It's a recipe for fraud and unscrupulous behavior.