Whether the other car has insurance or not is irrelevant to you. Your car insurance is going to pay or not pay based upon their internal policies.
What the other car having insurance does is give someone for _your_ insurance company to sue to recoup their money. Most individuals aren't going to be worth sue-ing, but other insurance companies will be. And most major insurance companies are going to have in-place agreements so that litigation isn't actually necessary (because it's more expensive).
The other vehicle being covered by insurance is absolutely _no_ guarantee that _your_ insurance won't decide to declare the vehicle a total loss. I myself drive a 2004 corolla that's had a salvage title since the mid-2000's due to someone hitting me. I chose to "buy" the salvage title from them and that vehicle has been 100% solid. They scrapped it because they didn't want to fix the body damage.
The insurance have had their cake and are eating it too. They're not required to cover you, but you're required to be covered.
I experienced once a minor car accident where another driver did some damage to my car (well, and his). There where no courts involved. Just one insurance company retrieving a bill (not mine because it was not my fault as the other driver and me agreed on (and used a form to confirm that) and paying the bill.
And my point is less about _who_ paid, but more about that _anybody_ pays. If two people without insurance hit each other, who's going to pay the bills?
if two uninsured people hit each other then they sue each other, they come up with an agreement on money exchange, or they both go about their business and pretend it didn't happen.
at least in the US, the only difference between two uninsured people hitting each other and one or both having insurance is the party doing the suing changes.
of course, injuries complicate matters but it's all roughly the same. Someone has to pay, which likely means litigation without a gentlemans agreement.
But if someone doesn't have insurance what's the chances that you suing that person is going to actually recoop your money? right, probably not going to happen. That makes it a business risk for insurance companies that end up having to fix their customers car but not being able to recoop that money. So they convinced law makers to require insurance so the chances of that happening are far less.
^ to better explain what I was trying to say before.
People will pay for uninsured motorist protection and _under_ insured motorist protection. under insured typically means an injury happened but the other persons insurance policy doesn't cover injury (liability) or the medical bills exceed what they do cover.
Think about that racket. They insure you but don't want to insure you without being able to fully recoop their money so they charge YOU to cover the case where the other drivers insurance won't cover it all.
it's a frickin' racket. If it's required by law it needs to be covered by the state or the insurance companies themselves need to be required to cover it. Anything else and it causes undue harm to everyone, most especially those who cannot afford insurance in the first place.
While there may be downsides, I'm happy to know that if a car hits me or my car, there is an insurance who pays (and it goes not to my insurer).