That's the crux of the issue though, you have granted the Wizard several benefits that he does not have - spellcasting is not subtle, so the somatic component there is dodgy, and mumbling is straight out (and depending on the spell, you have possibly given him a free range bonus and removed the material components too). That Wizard is clearly and visibly spellcasting, and that changes the scenario significantly - in the analogy he as the very least has his sword in his hand (and very possibly a very large cannon).