I think what they're speaking to is how such a change may alter the course of a presidential campaign. As it stands, there's this notion that a candidate has to try and have broad appeal; they need to spread their campaign out a bit in order to "capture" the electoral votes of a state.
Sans the electoral college, I see presidential campaigns becoming even more polarized and exclusionary. The Democrat campaign will become the "big city loop." Continually visit Los Angeles, San Francisco, Chicago, NYC, and Miami. Maybe they slide in a few secondary metros if it's convenient. The candidate won't have to worry about any non-urban messaging, and if they're particularly incendiary could even preach "dumping those hicks in the sticks."
Conversely, the Republican campaign (not even considering the existing insanity) becomes "everywhere else." They can push the message of "big city Democrats want to destroy you" even more convincingly.
Such an outcome strengthens the "not my president" sentiment (on either side), and just further aggravates partisanship. I'm not saying eliminating the electoral college is a change that could never be made, but I definitely think this is a bad time. It will feel like exclusion and alienation and in politics perception is reality.
For the obvious follow-on question "when is a good time," I don't have a pat answer and I can't even speculate if that will be in 4, or 12, or even 20 years. But it needs to be a time when there's far less immediate friction between the two leading parties, or it's just going to be another wedge opening the divide.