In 5e arcane spellcasters need only one free hand to perform somatic component. Which can even be overcomed with dual-wielder feat, which allows perform somatic component while wielding two weapons.
Weapon and shield though, yeah, arcane spellcasters just can't cast spells with somatic component while wielding both (no one can actually)
War caster allows you to cast with full hands. And the work around is burning your free action to draw/sheathe something in your hand to allow you to cast. They never have a weapon in their main anyway so its just a shield. Mainly comes into play with clerics wearing heavy armor, a shield, and a mace. They go in, attack, free action sheathe, bonus action healing word. Only downside is AOO is with fist, but who really cares. Next turn cast, draw weapon, repeat.The economy makes it so war caster is primary giving you AOO with spells and advantage con checks. The casting with 2 hands is fairly superfluous if you know the free action rules.