By that logic, also the CO2 footprint of manufacturing and transporting the fuel for an equivalent ICE vehicle, which is always conveniently left out of such calculations.
And also the footprint of building more generation stations (big) or building “renewable energy” generation (even bigger), which also conveniently gets left out.
The greenest choice most of us can make is an old, used car with reasonable emissions and that’s fuel efficient. Like a 15 year old Civic or Corolla. Or do what a colleague of mine did - he revived a first generation Prius, flashed newer software onto it, and salvaged a battery pack from a newer, wrecked Prius.
As pointed out by other nearby comments, that is not the greenest choice (which is to not drive), nor even the second greenest choice (which is to replace your ICE with a refurbished Prius like your colleague), or even the third greenest choice (which is to buy a new EV), but only barely beats out the worst non-green choices (buying a new ICE) and then only if you pay to make sure the car emissions controls and engine aren't becoming rusty and inefficient. Here's an article explaining: https://www.topgear.com/car-news/electric/mythbusting-world-...
There are also the caveats you mentioned that the analysis does assume that an EV is actually the greener choice, which is itself a function of a lot of other choices being made green also, such as whether it was constructed and powered with the most environmentally favorable choices of mining and manufacturing, most of which isn't really in the consumers direct control.
The actual scientist doing the calculations in proper LCAs do include this and production of the fuel is a notable chunk of the CO2 running cost of an ICE car (about 25%).
Relevant phrases are "well-to-tank" and "tank-to-wheel" which combine to give "well-to-wheel" numbers.