Except that it is a rule. The PHB/DMG is very specific about what is part of the action economy, dropping what you're holding, is not.

As such, you can strictly RAW, drop your weapon as part of any other part of the action economy, why would it not include the reaction? You can however absolutely not pick the weapon back up as part of the reaction, cause that is a free object interaction, which happens during your action or movement.

That said, I just give out that part of warcaster for free in my campaigns for the people that go sword/board+magic because I find it silly to force all those players to either do weapon drop shenanigans or force them to take a feat.