There is nothing as intense or ruling as the MOT in the US.
Depending on where you live (not every city requires this) cars must go under emissions testing every other year. https://en.wikipedia.org/wiki/Greenhouse_gas_emissions_by_the_United_States
As for the car's roadworthiness that the MOT test for, the US does not test for this as long as the car can go above 55 MPH, has the correct front and rear lights in working order, and can actually drive, that is seen as "good enough".
Unless you sell a vehicle and transfer ownership then there is need for (certificate of inspection) COI right ?
No, you can sell any car, any time, in any condition. All the receiving person requires is the keys and title of the car. To drive it on the road, the car must visit the DMV which is then retitled in the new owner's name.