The question: "What is the fuse protecting?" is really an important one, as it determine what type of fuse is to be used.
It is an important question but you also have to know how it is achieving that goal.
The primary purpose of the fuse is to protect the user from thermal injuries from an accidental arc-flash event. Without rehashing the entire process, an arc-flash may develop when you short out a high-energy mains power source, typically three-phase 480VAC service panels or other areas with high power connections. The arc-flash is essentially a plasma cloud that continues to short out the source until the power is removed by an upstream protection device or the whole thing explodes or burns down. This accident can happen if you mistakenly connect your DMM to a high-energy source with the leads in the current jacks and this is the scenario where the fuse is intended to step in and protect you from your own stupidity.
There are two places where the arc-flash is likely to start--at the tips of your probes or within the fuse itself as it blows. The arc-flash doesn't form instantly, but takes a few milliseconds to grow to the point where it continues. If you can interrupt the fault quickly enough you will hopefully avoid the arc flash. The fuse itself is sand-filled and designed to contain any arcs that arise within it. However, the only way to protect the user from an arc-flash starting at the probe tips is to interrupt the current flow very quickly. The typical 11A fuses used in Fluke and other decent DMMs has a rated "total clearing time" of 10ms at 200A. This presumably decreases with higher currents, but the chart bottoms out at 10ms so I suppose nothing is guaranteed past that point.
Multimeter-specific fuses are not unique regarding clearing time. There are other specialty fuses that behave similarly, such as solar protection fuses and other "fast" fuses that have a 1kV AC/DC and 10kA+ interrupt ratings. Fuses with lower interrupt ratings are not going to perform as well regardless of their time/current curve because they will have a longer arc time.