In most parts of the US, liability insurance to pay for damages to someone else's property or for injury to someone else, in an accident where you are at fault, is mandatory. You usually have to show an insurance certificate or card from your insurance company to register a vehicle. I believe there are states that don't require insurance but I haven't run into one.

Enforcement after you get your registration is so lax in most areas that most people carry "Uninsured Motorist" coverage in addition to the required liability insurance, to pay for your own injuries and damages if an accident is caused by someone without insurance. In a few states, including Kansas, the uninsured motorist coverage is a required part of the policy you need for your own registration.

Kansas has a bill in the current legislative session to require insurers to notify the DMV if someone cancels an insurance policy or allows it to lapse, with an automatic suspension of the Driver's License of the registed owner. It probably will pass(?). Some other states have similar laws, but it's variable.

How much good this law, if it passes, will do in Kansas is a bit of a question, since some reports are that 15% or more of drivers don't have a valid driver's license at any given time. No unlicensed driver is likely to be insured. (I'll continue to carry my uninsured motorist coverage.)

Insurance rates are variable depending on vehicle type, equipment, owners' driving record, miles driven, and location. In some low-density areas, a vehicle might get minimum required insurance for $100/year or a little less, but in high traffic areas, it can run to $1,000 or more. With a poor driving record, it can go very much higher. If you want to insure the vehicle itself, for replacement purposes (required by most lenders if you finance a purchase), it can get "really pricey."

The only inspection of vehicles here (Kansas) is when a "foreign title" (from another state, usually) is presented for a first-time title and registration. About the only thing checked is that the "VIN" number on the vehicle matches the paperwork, although the inspectors do have the authority to cite for defective equipment. For "odd vehicles" like trailers, trucks, or RVs, they may look for a "gross weight" tag, since that affects which tables they use for tax purposes.

Since you have to carry the insurance, and many people pay monthly or semi-annually, most people don't see it as a cost of registration. The big "bite" here is that you pay the "property tax" on the vehicle at the time of registration, as part of the registration process. The tax rates are extremely variable by vehicle type, but are theoretically based on the value of the vehicle. My two >10 year old vehicles together cost me about $300 (US) per year. Some new cars may pay a couple of (or a few) thousand dollars initially, and generally all depreciate in actual value faster than the tax does.

(Note: if your purchase contract shows a "list price" and you later get a "rebate," the list price before the rebate is what is taxed, and is the amount depreciated for subsequent years. A 5% rebate, for a vehicle that you keep for 10 years, will cost you nearly 3 times the rebate amount in additional taxes over the life of the vehicle, when compared to the tax if the "real price after rebate" had been on the sale contract. Aren't those rebates a really great deal?)

John