It works pretty great! As you mentioned, the only downside to it is that people see zerks, and use grease. On my mill (which is all zerks), someone had pumped the machine full of grease as well. I suspect someone who just didn't know.
I wonder if the same happened to your machine. Someone swapped a bunch of cups (damaged one? Or just wanted to unify to match a mill sitting next to it?) for zerks, and went on oiling it. It passed onto the next person, who saw zerks and decided they needed grease. The rest is sticky history
In the case of my mill, I had to tear it down and use a bunch of pipe cleaners to get rid of all the grease. In your case, I think I would hose down the inside (aerosol degreaser would make quick work of it), then pull the ram to wipe it down.
The only one I'd be concerned about is the one above the stroke adjustment. Though, I suspect you could put some degreaser in a push-n-lube to force the grease out, and then just force some oil in behind it.
FYI, I JUST got my 7A as well, See
https://www.hobby-machinist.com/threads/new-atlas-7b-shaper.84336/ . You can see what I mean about the grease cup on the near-side of the main shaft. The only hold up I had getting mine running though was to make a vise!