It also makes visiting family , which is a big thing in Israeli culture and enabled by short distances, very annoying if you don't have a car.
Scooters and e-bikes "solved" a lot of these troubles inside the city, but infrastructure hadn't caught up - not enough bike lanes make it very dangerous and injuries and even deaths are not uncommon. The upcoming newly built intercity tram should theoretically also help.
Also, the lack of bus service during Shabbat means everybody needs a car just to go see their family every Friday, which then means you're a car owner and more tempted to create traffic the rest of the week. Since 2019, Tel Aviv mayor used a loophole in the Shabbat law - by offering busses for free they are able to run during Shabbat, but the area covered is small.
I don't expect it to help much with the Shabbat issue, but politics are hard to predict so we'll see.