Precision resettable fuses
As PlasmaHH commented, fuses are for gross overload protection. They are not remotely precision devices. Worse, since real fuses operate by thermal overload of the fuse element, their trip point depends on the required operation time. That is, there exists some current for which the fuse will blow after a very (theoretically infinite) time. For any current above this level, the greater the current the shorter the operation time. And the relationship is not linear, either. On the plus side, there is little effect from ambient temperature, since the fuse temperature is so high that the rate of heat loss to ambient is essentially unaffected by normal ambient variation.

Of course, you can roll your own. The conceptual circuit looks like







simulate this circuit &ndash; Schematic created using CircuitLab

Here, the load current is sensed and compared to the desired trip level by CMP1. The latch has been set by temporarily setting the S input, and the output is high. This drives the level-shifting transistor Q1, and the FET is turned on hard.

When the the load current gets too high, the comparator goes high, the latch is reset, and the FET is turned off until another RUN command is issued.

In principle, you can get sub-microsecond operation with extremely repeatable trip levels. 

The devil is in the details.