I don't want to play a caster with a shield. It's a complete flavor fail. But when the proficiency is there, it feels like I'm intentionally gimping myself if I don't use one for a better AC.
I really dislike the militia thing for humans and half-elves. It feels slapped on for mechanical reasons rather than flavor and verisimilitude.
Thematically it sucks, but at least when weapons are unsheathed for casters, if you have a staff equipped, you do not see the shield outside your character sheet.
The problem is that light armor and caster armor in general and staffs as weapons really have no incentive over melee weapons like shields and heavier armor. Staffs should have a passive granting more spell slots and spell attack roll proficiency for not wielding a shield and only wielding one staff in two hands. Light armor should increase saving throws and grant elemental resistances, while heavy armor users should not be able to gain effects like invisibility or blurr.
As it stands, there is really no reason to wear light armor when you have access to heavy armor.