Why not just air harden it?
Because with complex steel there is more to it than just getting "under the nose".
Steel manufacturers frequently recommend an interrupted oil quench (or salt quench) for HSS to optimize its properties.
Carbon movement is time and temperature dependant. Carbon is leaking out of the austenite on the way down, and will combine with alloying elements to form carbides rather than staying in place in the soon-to-be-martensite.
A rapid quench will reduce this carbon leak - achieving two things. A more carbon rich martensite, and more free alloying elements, which can be a good thing. And, through a mechanism that I don't understand, it will also result in less retained austenite.
According to the 5th edition of "Tool Steels", high speed steel in industry is frequently about 20% RA. That is after three high temperature tempers.
A property that is important to us, but less important to tool makers, is fine edge stability. A nice homogenous micro structure with hard martensite, little RA, and an optimum carbide structure and fine even grain will have the best edge stability. A rapid quench helps some steels achieve some of these properties (though no effect on grain size or primary carbides). Cryo as part of the quench, and avoiding the secondary hardening hump are frequently helpful as well, though I'm not sure about M4.
HSS is generally fairly low in carbon, and high in alloys. Its hardness in the secondary hardening hump comes not from martensite hardness, but from the formation of carbides which increase the overall hardness of the microstructure (though probably reduce edge stability).
M4 is about 1.4% carbon, which would usually be considered very carbon rich - but not when you consider the very high vanadium, tungsten and moly content. These will gobble up most of that carbon. So even with its 1.4% carbon, M4 is probably still fairly carbon lean because all the alloying. There is also something like 4 or 5 % chrome. A rapid quench will prevent that chrome from gobbling up what is left of the carbon on the way down.
So, it seems reasonable to me that oil quenched M4 will have harder (stronger) martensite, less carbide volume, and less RA and more free chrome (corrosion resistance), though I'm unsure how one would go about cryo and tempering to maximize the effect.
... my .02 on oil quenching air-quench steels...