It is done sometimes (I've done it). The issue, as Indraneel has said is that it's not very fast; so for example if your load becomes a dead short, something may blow up in the microseconds it takes for the current limiter to trip.
For the purpose of preventing overloads and other conditions that can be tolerated for a short time, MCU current limiting is very useful. I think it's done fairly often.
Most practical current limiters (like circuit breakers) have 2 limits. A slow limit which will trip if a slight overload is sustained for many seconds, and a second limit which trips very fast in response to shorts and extreme overloads. This keeps things from blowing up during shorts, and also doesn't erroneously trip due to motor starts or capacitor inrush currents.
In a home circuit breaker this is literally 2 separate mechanical systems, one is a bi-metalic strip, and the other (the fast one) is magnetic.
Basically your MCU current limiter is the slow type. Depending on the application it may need to be paired with another faster limiter.