I’m not a huge fan of the artillery, I only buy a few in a game.
It’s true that the same amount of money spent on Inf/Art will pack more punch than that amount spent on Inf/Arm. However, the Arm with their ability to blitz and move 2 spaces means they exert influence over a considerably larger area - a large stack of German Arm in Eastern Europe can strike at either WE or Ukraine, which will affect Allied play in both of those areas, even if you can’t do both it will deter attacks from both.
Also, if you are attacking with 8 Inf 8 Art (56 IPCs, punch of 32), every casualty means you lose 2 in punch. With 7 Inf 7 Arm (also 56 IPCs, punch of 28) you can take 7 casualties before your offensive strength really starts to decline. Of course you have 4 less punch to begin with, so maybe the Inf/Art are still superior offensively for that reason.
However, defensively an Inf/Art combination has 1 less punch than an Inf/Arm combination. And as I noted above, your Armor can add its potential punch to two different fronts. I love having a bunch of Armor in Ukraine, the Allies land in Eastern Europe, and the Armor swing back from Ukraine and wipe out the invasion force supported by Inf from Berlin.
Finally, if you are limited in production by the IPC value of a territory, you get more value building Armor. If Japan has a bunch of transports and ICs in India and FIC, they can build 6 Arm on the mainland and shuttle 4 Inf to Persia every round, which puts a lot of pressure on Russia.
With Germany though I usually buy 1 or 2 Arm per round as needed so I can buy maximum Infantry with the rest without having any money left over. Then, once you have a substantial amount of Inf to start moving forward, I start buying more Arm than Inf.
Mostly it’s the tactical value of the speed that makes Armor much more useful than Artillery.