Been watching some of the runs for this game, and I noticed that Mog's magic never seems to be used. Do the elemental charge combos not do extra damage? I know it's not practical most of the time, since Mog's range is so tiny, and Mog has to drop the chalice to cast, but I would imagine it would help DPS on stationary bosses.

This is nested problem unfortunately. The short answer is that it's too slow and is weaker than just hitting the enemy and Mog is unfortunately just not good.

Magicstrikes or elemental focus attacks o whatever you want to call them, end up being much to slow to be of use, given that normal triple-a inputs are usually faster and more damaging anyways in most situations. (The only time it's not is when a character's STR is too low to break past the enemy's defense, and the FA would put them over that character's defense.)

The specific damage formula for a spell fused focus attack is: FA Damage * X, where X is the number of people casting the spell that was fused. In the case of singleplayer and Mog, this means a value of 1 for X. Basically it doesn't do any more damage than it normally would in singleplayer. It also has the problem of needing you to either menu through and set up a magicstrike on your Command List (likely foregoing a Phoenix Down, a really bad idea,) and that it takes extra time to release over a normal, already inefficient Focus Attack.

The one advantage it has is that it's strength in terms of applying status effects is rated at Fira/Blizzara/Thundara levels, which means a certain few bosses can be lit on fire for it (Armstrong from Tida). In practice, this is still a time waste given that the resulting flaming debuff barely lasts long enough to get a few hits off.

Mog's spells are also extremely random, and if I remember right, painting him has little to no effect on what he uses. He also has an internal MAG of like 6, so anything he casts does about 1 damage. I believe there are strategies used by the TAS to deal an increasingly minimal amount of extra damage with him though.

The magic strikes are cool, I wanted them to be good, believe me, but they're just not going to work in the speedrun.

Even in a TAS, I prefer using the normal spell from Mog instead of the fusion ^^ The only possible useability of Mog's spell fusions would be firestrike against some bosses, but due to it's rng nature (and the fact ultimately it's not worth) nobody would use it.

Best use of Mog would be in magic-users category

Yeah relying on Mog for any type of spell fusion is too unreliable to begin with since which spell he casts is random.

You can get him to cast a normal spell on a boss for a tiny bit of extra damage, but this probably doesn't actually save any time outside some very niche potential scenarios, if at all. Mog's damage is just way too negligible to be worth the hassle, so much so that one of his spells probably doesn't even save a hit on the boss later in the game.

We've thought about magic fusion before in places like Tida since a firestrike can burn the boss (the firestrike itself doesn't deal more damage than a normal focus attack, but while the boss is burning its DEF is lowered). However, the menu time and needing to focus attack to apply the buff makes it not worth it over just attacking normally. Assuming he casts Fire, fusing with Mog would skip the menu time, but then you have extra animation time required to just do the attack so it still isn't any good.