Thrown weapons tend to be small and lower damage but the rules as they are will apply equally to larger improvised weapons without the thrown property. I would have preferred the draw throw draw throw ability to be linked to the thrown property itself.Throwing weapons seem like something one definitely wants to support. I throw a dagger. Then another (different) dagger. Then another. Etc. Maybe I have a whole bandolier of daggers. I can equip one as part of an attack action, and provided my hand is free it seems common to allow that I can equip another as a free interaction. Throw > draw > throw > draw > throw. I don't see any text that specifically prevents a character also wielding a shield while doing so.
What I would most like to see in some sort of future Sage Advice, would be clarity from the game designers around how they see shields and "different weapon" mattering to game balance. And if they don't, then offering a reading that gives players greatest choice over how they picture their characters.
I'm not a fan of drawing as part of the attack being universal to all weapons tbh. So much cheese exploded on day one and I dislike doing dumb artificial stuff for purely mechanical benefit.