Poor people are probably using public transit, not driving in the first place. Investment in public transportation would be good for them. Investment in roads (automobile infrastructure) benefits only those who can afford cars.

So it is more expensive to pay a one time fee to deliver the fridge (which a lot of companies do, or make it free), than to own and run a car?

What you say may be true in US cities, or in the countryside.

For me, living in Tokyo, it is really cheaper not owning a car but renting it when I need to, or hiring a delivery service. I guess that the same happens in most major European cities.