Compared to standard slot screwdrivers, Phillips was a godsend. Slotted screws are easy to make, as are the drivers, but the drivers slip out the sides easily. Hollow ground drivers are the best for fitment. Keystone and Cabinet drivers don't fully engage the screw and can damage them. This is why gunsmithing sets have so many hollow ground drivers or bits. On firearms, there are a wide ranged of sizes, and replacement screws can be hard (or impossible) to come by.
Plus standard drivers only have two positions available, where as Robertson and Phillips have four, making it easier to get the driver into position. Allen and Torx have 6, which is even better, but above that, the law of diminishing returns kicks in.
Snap-on and a few others use Phillips ACR tips which have little ridges that grab the screw. Diamond tip drivers work pretty well but both of these can damage a screw.
Also note that the Phillips standard has changed a few times. A modern Phillips is closer to JIS than older style Phillips drivers.
Slotted screws back when they were hand made, routinely had the slot cut into the screwhead using a “knife file”.
Knife file are wedge shaped in cross section, producing a tapered slot.
Screwdrivers, or turnscrews, as they used to be called, made with tapered flat heads, fit the tapered slots made with knife files excellently.
You can literally just push a tapered flat head screwdriver into an old screw whose slot was cut with a knife file, and the screwdriver blade will wedge itself in place, like a Morse Taper in a Morse Taper socket on a drill press.
If a screwdriver has too fine a tip to fit the screw, you just file the tip back slightly.
The tapered sides on “Keystone” shaped tapered flat head screwdrivers can also be easily filed if the screwdriver is too wide.
The design worked really well for the old hand slotted screws.
I’m not sure when gunsmiths started using very narrow slots on screws, and when they started cutting those slots with something closer to a saw blade rather than a file, resulting in narrow, parallel slots.
For regular screws used for cabinetmaking and carpentry, the change to non-tapered slots on screws seems yo have happened around the time screws started to be mass produced by machines.
The parallel slots are generally a worse design.
The hollow ground screwdrivers for those slots are weaker, and don’t serve as good as a general purpose tool.
Incidentally, taper ground slotted screwdrivers will still work decently with parallel slotted screws, if used right.
If the tapered tip is too narrow, you file the tip back slightly till it just doesn’t bottom out.
The better tapered slotted screwdrivers like Facom usually have small grooves on the tip, that I think are cut with a checkering file of some type. (usually finer in the line than what was typical on similar US made screwdrivers)
A tapered screwdriver that is sized right will stick out of a horizontal turned slot on a screw, that is screwed into a wall. At least I’ve done this with Facom slotted screwdrivers that might have been 12” long.