Yup, but many manufacturers are carbon-offsetting their production a lot more compared to ICE cars.
Also: depending on your country's electricity production profile, EVs tend to become more environmentally friendly around 2-3 years of use according to studies.
And when the production profile changes (more renewables etc.) ALL EVs on the road instantly become better for the environment. There's no practical way of makin ICE cars better for the environment after they're sold.
For sure. I get annoyed when people argue along the lines of "but look how all the power is generated using coal and oil" because people simply don't understand that electricity is the interface that decouples the car's energy source from the way its source. As you said, once electricity is generated using only renewables, bam, instant success, without changing anything about the cars.