World's response to the climate crisis is already dangerously delayed, and we're at a point where we need anything ASAP. We've ran out of time to massively overhaul infrastructure everywhere.
The US and UK apparently can't even build a single high speed rail line any more.
Car dependency sucks, but we won't be able to fix that in the short term, but at least we can fix its oil dependence.
Cleaner grid will also need a lot of battery storage, and EV demand helps scale that up.
I don't think it's a particularly different timescale to swap from ICE to EV than to drastically reduce car dependence. What makes you think there's a big difference to where swapping to electric cars is easier than avoiding cars?
Credible reduction in car dependence needs well connected fast passenger rail networks, and changing urban sprawl to something denser with more local amenities.
The first one is a major infrastructure project, the latter is largely unpopular with the people already living there (and Republicans react to the concept of 15-minute cities like it was a gulag).
Infrastructure is still built as if it was business as usual, so can easily get blocked and delayed by decades on budgeting, bidding, consultations, NIMBYs, environmental surveys, etc.
OTOH we've already got EVs, we have already been building infrastructure for them, and it's a smaller change more acceptable to people.