I always thought the justification for this was that wizards trained for the Wizard Wars were trained differently to the typical wizard (e.g. the ones from original Magicka). They weren't trained for super-heavy invocations of heavy spells and tremendous Magicks, they were trained for agility, versatility, and close-quarters combat.The Wizard Wars are a repeating event (every 10 years perhaps?) with the purpose of establishing the top wizards. To force the lazy wizards use their 'skill', powerful magicks are cast to limit other magicks to the strange and abstract 'focus bar', limiting the number that can be taken to battle, while only 3 elements can be put into a queue and Q and R, and Q and F, don't collapse into a single element to avoid the use QFQFASS, or some variant. Also, all other spells are balanced (well, supposedly) to make all the spells more viable and increase the skill level required to reach the top.
This shows in stuff like how these wizards are able to move while casting, beams have limited range, arcane takes precedence over lightning, they require focus to cast Magicks as opposed to elements, their "world ending" Magicks are restricted to a much smaller radius (think Thunderstorm in original Magicka versus Wizard Wars).
The wizards shown in Magicka 2 may have received training from both groups of wizards and thus can use super heavy spells and do their stuff while moving.
Or at least that's just me reading into what's probably balance and programming restrictions.