Republicans are totally comfortable with the EC enabling minority rule, winning the PV is not a priority at the moment for them so it won't happen until the EC stops enabling them, maybe if Texas goes blue in the 2030's they'll finally have to expand their appeal with a more moderate challenger, that's when they'll next win the PV.
The EC rewards winning states (and votes) from a wide range of places and regions in the country. The overall popular vote itself is less relevant than where you actually get those votes. The GOP has a relative advantage there under Trump coalitions, while they were at a disadvantage in the Obama-era ones.
I agree that the GOP will broaden their appeal in those circumstances and likely win the PV.
The EC empowers states like Montana and weakens states like California, basically rural votes matter more than urban votes, which is nothing but good for the GOP.
The EC provides at least as much of a penalty to those whose support is strongly concentrated in one region with blowout margins (like the Democrats under the post-Civil War party system till 1932).
This could be seen in 2012 as well. Romney won blowout margins in many places in the West and did well in the South, but Obama was firmly in control in the tipping point states.
Yes, it's not at all impossible for the EC to favor the urban coalition. If Dems got their L.A./Chicago/NYC margins in Miami, Houston, and Dallas that would be the case today.