It should, obviously, but even today (with not so great energy mixes) electric cars do better than gas cars from an emissions point of view (even if looking at the whole life cycle).
Electric cars are energy mix agnostic and you try to frame that as a disadvantage but it actually is not, quite the opposite. They are one puzzle piece that enables change and without which change is not possible.
I don’t get arguments like yours.
Obviously we always have to do much, much more. We have to massively push individual cars out of densely populated areas and turn them into an option that is not fun at all to use there. We have to upgrade public transport. We have to better our energy mix. Buildings have to become more efficient on a massive scale. Energy intensive industrial processes have to transition to ways of doing things that can at least be plausibly made CO2 (equivalent) neutral like hydrogen. And and and. Doesn’t mean that all of this has to or even can happen at the same time.