This is nonsense. A tool of focusing magic in the shape of a staff can be damn well anything you please because it's not a real thing and you could absolutely just go "yeah it's made of gromril or cold iron or my magic metal that's why it works and also why it's perfectly suitable for caving in that dude's head despite a helmet".
Fiction is not subject to game balance concerns! Wizards are allowed to have both traditional aesthetics and be good in melee if you feel like it!
Now don't make me get Subaru Nakajima, a literal punch mage, who literally delivers magic half the time in the form of hitting things with her fists, in here.
It's not a matter of game balance, at least not for me. It's that it's a common (not universal, but
common) rule of human endeavor that a well designed tool is optimized for one thing in particular, often at the expense of its capacity to perform other things.
You can try to use a flathead screwdriver as a chisel or a chisel as a flathead screwdriver, but in either case you are likely to be less than thrilled by the outcome. You can try to use a knife blade as either, but the result may be even less positive. To me,
in general, on average, it would stand to reason that an optimized tool for amplifying or enabling spellcasting would probably not be well suited for use as a blunt instrument,
most of the time.
You can absolutely write a story where there's an exception, where the optimum tool for a particular magic-user is a large bulky piece of metal, let's say.
Or where what matters isn't that the 'staff' is optimized so much as that it has a close personal connection to the caster, oh and the caster is a shepherd who happens to be the strongest guy in the village and it's the hardwood quarterstaff he carried before he found out about his magic, so you really don't want him hitting you with that thing. That one's my favorite.
But these would, to me, be exceptions, not the norm. Typically, there's some effort to make a narrative justification for
why the magician is using a magical instrument that also doubles as a heavy blunt instrument and is reasonably skilled in using it for hand-to-hand combat. Absent such an effort, well... a man who has good reason to carry a knife blade everywhere
may use it as a chisel when he's desperate, but he can't very well act surprised if it doesn't work well or breaks when he makes the attempt.