Does the Eldritch Knight need the Warcaster feat to cast spells when using 2h or sword/shield?

Many of the spells that an Eldritch Knight can cast have a somatic component. If I am playing as an Eldritch Knight with a two-handed sword or weapon/shield combo, would I require the Warcaster feat?

The way I see it is that the Warcaster feat’s intention was to allow those with two-handed weapons, dual wielding or sword/shield setup to cast spells, meaning that by default, Eldritch Knights shouldn’t be able to cast spells with somatic components without the feat.