How to precisely cap current
The only way to clamp or cap current (same thing I believe) is to power the motor through an electronic speed controller (ESC). With a DC motor, limiting the current is pretty much the same as limiting torque. Once the current limit is reached, the limiting will reduce the voltage to whatever value is required to hold the current at the set level. It that means reducing the voltage to nearly zero and stopping the motor, that is what must happen.

An alternative to a fuse would be an overcorrect trip that would shut off the motor in the event of excess current. A high quality ESC would have that as an alternative built-in. It could also be accomplished electronically without an ESC.

Both options could be fast accurate and reliable. Neither would address every safety concern. Some situations would demand human access restrictions.

AC motors could have something similar.