Apparently this Field Artillery relic from the era of steam gunnery has drawn the same conclusions as me. I am sure @FJAG will agree with his fellow gunner.
I actually don't agree entirely with him.
I fully agree on math. Artillery lives and dies on trigonometry. I've mentioned before that I never understood it in high school but during my second phase of basic arty offr trg the lightbulb went on and I started to ace trig and log tables and slide rules - you name it. It suddenly all made sense.
I never understood why the Americans adopted or stayed with the azimuth system when the bearing system is so much simpler to implement. True story, the M777 works on the azimuth system but Canada adopted the British LINAPS -based digital gun management system to digitize the gun thus staying with the bearing system. The Aussies opted for the American digital fire control system and consequently were forced to change from a half century of using the bearing system to the azimuth system.
That leads me to part three about math - math is garbage in and garbage out. There's There are many parts of the equation that he doesn't go into - cost per round is one.
A critical one is survivability and redundancy. If one HIMARS pod lays down the fire of a canon battalion 1 Rd FFE then if you lose one HIMARS, you lose a battalion's worth of support. Basically the "all eggs in one basket" problem. So at its most basic it would be silly to replace a cannon battery with just one HIMARS - you'd need several.
Then there's the basic load he talks about but let's simply look at each gun's in-turret ammo - say 30 to 40 rounds. Once a HIMARS fires its pod, it's out of action and needs to bugger off for a reload which takes time. A canon battalion can fire the equivalent of a HIMARS pod (give or take based on his figures) but then it can fire another and another and another (you get the point) for up to 30 or 40 times. If like the US it has M992 then there are another 93 ready rounds at hand. Yes - you probably want to move the guns as well but with 18 guns you can move some while you keep others in action providing continuous support - a single HIMARS can't do that.
Then there are ammo types. I have yet to see a HIMARS illuminating or smoke round. Interestingly, to lay a linear smoke screen or multi-pattern illumination mission you need several guns and while its technically feasible to create these ammunitions for HIMARS and maybe even work out the technical solution to ripple out the pattern required, no one has done it yet.
I'm far from being the dinosaur who wants to keep horses, which he seems to relegate gunners who disagree with him to, I'm a firm believer that you need to do a lot more math then he has done. There is not only room for, but a necessity to have a broad mix of mortars, guns, rockets and UCAVs as part of the indirect fire mix. Add in missiles and lasers and EW for air defence and UAVs and radars and even audio sensors for STA.
Incidentally at the RCAS, they do teach meatball, handraulic indirect fire calculation for when the electronic stuff goes down, but there are some trades - like the old surveyor and survey offrs course I took - that're no longer in the mix. That makes it tricky to do some of the higher order work needed to couple multiple batteries and regiments together if we lose GPS and the like. Not impossible - just hard.