This is more complicated than you are presenting. GWM is a feat and if you start bringing in feats you run into all kinds of scenarios. The extra damage varies widely with AC and attack roll, and it takes a BA for the most powerful part of it (which is the negative for TWF). Letting the GWM get his free attack for free without using a BA actually makes the difference between this and a TWF larger, not smaller, unless you nerf the feat and take that away.My point is you described a sequence of events that is objectively worse than using a greatsword. You got +0 damage in exchange for having to track your 1 free Interact With Object (oops, there's something else that isn't a bonus action or action) and your dropped weapon. Not to mention that you need two magic weapons instead of one. I guess you could take the DW feat...but greatsword + GWM is still better.
I made note of this, because so far, all objection that letting dual-wielding warriors always make all their attacks breaks the game really is long on claims and short on evidence.
There are all sorts of reasons to have a weapon in each hand, what if one is a staff of defense, or one has a reach like a whip for AOOs but worse damage than a shortsword that you are going to use as your primary weapon.
I agree dropping a weapon to cast a spell is objectively worse than using a greatsword, but that isn't my point, you were arguing that a person wielding 2 weapons would not be able to case a somatic BA spell, and that is objectively not true. If TWF is part of your attack action and there is no cost for bonus actions, they absolutely can do this.
Again you are mixing up dual wielding and TWF. There is nothing RAW which prevents dual wielders from making all their attacks, it only prevents them from getting an extra attack (one more than they should get) unless they spend their bonus actionI made note of this, because so far, all objection that letting dual-wielding warriors always make all their attacks breaks the game really is long on claims and short on evidence.
Further RAW you can even do TWF and still attack with a great sword (assuming you have extra attack). IF you start the turn holding 2 hand axes, you can attack (or throw) one of them, use TWF to attack (or throw) the other, then drop anything left, draw your greatsword and attack with that. That is totally legal RAW. It is not specific to hand axes, you can do that with daggers, a dagger and a short sword, scimitars, or if you have dual wielder any 1-handed weapon.
The constant in all of this is the extra attack uses your BA.