Here's how it works: You pay a sizeable chunk of money each month to the car insurance company, because it is almost certainly not legal for you to not do so.
Then your car gets into an accident.
If the other person has insurance, you get to endure a lengthy, tedious, possibly formal court room dispute about which person is at fault and who's insurance pays for what.
If the other person doesn't have insurance, they will probably flee the scene and you may not even be able to prove to your insurance that it wasn't your fault, or that your insurance is liable for anything.
If the damage is significant, It will almost certainly leave you without a functioning vehicle for weeks or months, and this is rarely compensated, enjoy your carless commute.
Also, in all these situations, unless you are paying significantly for actual insurance with good coverage (don't mean to be rude but you're driving a Hyundai Elantra so probably you can't afford that), then what you are paid in compensation will be about 50 to 75 % of what the repairs will actually cost, and/or the mechanics doing the repair will not fully repair your car or fuck up some other part of your car in the process, so you basically have to learn how to do their job for them to doublecheck their work.
Thats how cars and car insurance work in America, if you want an explanation from anyone who isn't a car mechanic or car insurance employee.
EDIT: Oh, forgot some important things:
Post accident your monthly rates will almost certainly go up, doesn't matter if it wasn't your fault.
Also if you or another person were seriously injured, you, as a most likely fairly poor Hyundai Elantra driver most likely unable to pay for substantial medical coverage, will now get to endure another unimaginably stressful battle between car insurance and now also health insurance and hospital billing teams, which is highly likely to result in you being personally liable for either your own or the other driver's medical costs.
Potentially while you are in a full body cast, in a hospital, about to be fired from your job if you don't completely heal and get back to work in a week or two.
Or passengers, or pedestrians could have been injured, both of which are basically silo'd into optional dlc for what you thought you (and the other car owner) were paying for but actually aren't, unless you spent multiple hours going over the fine print of your insurance contract, but even then it might not matter as insurance agencies themselves decide what they cover, and you would have to sue them, with even more money you don't have, to attempt to get them to follow their own contract if they decide they don't want to.
Oh and property damage to not your car and not another car (say you crash into a storefront or run over someone's fancy phone and they sue you over it, or back into something and damage it) is its whole own other silo as well.
Oh, and if your car has a manufacturing defect which causes a failure, you're also basically SoL in terms of your insurance covering repairs or replacement. Car insurance doesn't usually cover that whatsoever.
That's all between you and the dealer and the car manufacturer and you keeping up with regular updates on your specific model of car.
Oh you bought it used, personal title transfer, no dealer?
Almost certainly SoL from a warranty (or total lack thereof) perspective.
