A Mini is a BMW underneath, and it inherits both the good and the bad of that.
The petrol Cooper and Cooper S use BMW’s three and four-cylinder turbo engines, which inject fuel straight into the cylinder. Nothing washes the intake valves, so deposits collect there — and because a Mini is small, light and usually driven in town, they collect faster than the kilometres suggest.
The Cooper D has a particulate filter and an EGR circuit, and a car this size is very often used for exactly the short trips that block both.
A Mini also hides its symptoms well. The engine is willing enough that owners put up with a rough idle for a long time before anything gets looked at.