
The real reason mages use staffs (picture is a giant spoiler for the golden land arc)
Certain spells can blow back and injure the caster. Especially if the caster is running low on mana or has bad mana control and can't protect their hands.
It would also make sense why you start off apprentice mages with staffs. You don't want a kid accidentally blowing off their own arm if they mess up a spell. Then from there it just probably becomes a habit for most mages to keep using a staff.
The mages we see not using staffs in current day are Richter; a mage who doesn't use energy based attack spells. And mages like Falsche and Sense who also don't use energy based attacks. (By energy based attack spells I mean a spell that creates a substance that's directly destructive ie. Zoltrack, Vollzanbel, Judrajim, Catastravia, etc.)
Genau is the one exception who does use an energy based attack spell with his hands but we only see him use that spell as a quick draw attack we never see him use it in serious combat.
Mages like Flamme and Serie have enough mana to where they would never have to worry about accidentally injuring themselves. But even then Flamme still doesn't shoot the spell we see her kill the three demons following her and Frieren out of her hand. The spell she cast appears instantly on top of her opponents. The spell itself never actually goes near her.
Serie can be disregarded since she has so much mana and her mana control is so ridiculously good it would be nearly impossible for her to be damaged by her own spells.