As I see it, Wardens have swords for that very reason. Using magic all the time simply isn't feasible.
Some people will let you take a stunt that adds a mental stress box. Whether this is balanced is an open question.
It's probably sensible to say that self-inflicted harm from spellcasting automatically satisfies catches. Which makes wizards with Recovery a lot more reasonable.
There really isn't any precedent for a stunt to increase someones stress, and it strains the confines of what a stunt normally does... The biggest problem is the extra stress is variable... It could end up being the third, fourth, or fifth stress box, which would make it stronger and stronger, something that no stunt to the best of my knowledge really does. The best you could do is convert the No Pain, No Gain stunt into a similar one for a Mild Mental Consequence, with the current set of rules... Hendricks has a kinda similar stunt on his character sheet, called I Have a Job to Do, or something like that, that lets his mental stress be determined by his Discipline, rather than Conviction. Kinda sets a little bit of a base, that the books just don't add copy's of stunts, due to word count and such.
Btw, that stunt, as well as Person of Conviction bot allow you to use one skill instead of another to determine your stress capacity. If you get that skill to 5, would you also get the Mild Consequence as well, or would that only be granted through the original skill?