Not sure if you're a student or never had an income, but savings are not just for retirement. Savings, as opposed to a retirement plan, are for major life decisions like buying a car, getting married, supporting a family, upgrading your standard of living, taking care of emergencies, and affording expensive opportunities (like moving or traveling, for instance).
Also, no, the basics of supply and demand will not make cheap cars a thing. It's not the cost of a car that you can't afford, it's the cost of maintenance. Fuel, maintenance, and insurance (mandatory in the US btw) are all costs to use the car - the average being around $100/mth.
https://newsroom.aaa.com/tag/cost-to-own-a-vehicle/ -> 1.1k
And also no, new cars will not become cheaper over time in the US. There's already 19% of the US families who make under 24k a year (we roughly double UBI to account for 2 adult UBI incomes and one car per household rule). That's 24 million households already out of the 130m households in the US. The market for used cars is actually quite big (17.6 million transactions / yr) which is probably why there isn't an $8200 new US car offering (which, btw, requires savings in order to purchase).
Back to my original point, if you have a budget of 1k/month, you could spend ~$400 on rent, $300 on food, $100 on your car, $100 on personal needs, and $100 on misc / emergencies in a small suburban town (like the outskirts of Pittsburgh) -> I've done this in college before. But realistically you would need an extra ~$600-1000 a month to pay for things like - internet, health insurance, furniture, clothes, laptop, phone, heating / ac bill, eating out every so often, a social life, hobbies, travel, etc. So yes, you'd still want double of your UBI income.