There is no Facing in D&D. You are considered to always be looking and spinning around, facing enemies that attack you. Thus, a shield only provides +2 AC when actively equipped, being used to block attacks. Dual Wielding doesn't naturally provide any AC because you haven't trained to do so. There's an entire feat representing that training (just as there is a feat you can take to get proficiency in Shields).

Otherwise, if shields provided +2 AC while strapped on your back, then every class with shield proficiency would be able to always get +2 AC. But if you continue this line of thought: as it requires no skill to strap a shield on your back, why does it even require proficiency? Why can't any random schmuck do this? Essentially we've just increased every creature's AC by 2.

To prevent a free shield bonus in BG3 (which, imo, is the real problem of the free unlimited weapon swapping), the RAW solution is to make switching to/from a shield should require an action. Every other weapon swap could be free. Shields should only provide +2 AC when wielded.

But if we want to reduce that penalty a bit, one of the following might be appropriate:
- swapping to a shield could take a bonus action
- you could only get 1 free weapon swap per turn, preventing you from always switching to a shield-weaponset at the end of your turn
- perhaps your weapon set is locked in once you make your full attack (all attacks granted to you by your X Extra Attacks, including Haste actions)