No, you're still not getting it. RAW answer to that is same than to the question to what happens if rogue adds sneak attack damage to a great sword attack. There is no answer, because that simply isn't allowed by the rules. Rules don't allow druids to to wear metal armour so question 'what if they do' isn't covered by the rules.
There
is an answer to what happens if a rogue uses a greatsword in a sneak attack: they don't get sneak attack dice. They can still attack from stealth, likely giving them advantage on the roll.
So since you refuse to answer this question, let's change it a bit: what force prevents a druid from wearing metal armor? Tradition? PCs often scoff at tradition. An oath? Then what happens if they break the oath, and why is that not listed as an oath like with paladins? An invisible sprite that follows the druid around and attacks whenever they put on metal armor?
I understand not liking this. I don't like it either. What I don't understand is not understanding it.
I don't understand how you don't see that it's nothing more than badly-worded fluff with no actual rules attached to it.
Wizards can't cast spells in armor. Why? Because they're not proficient in armor. If a wizard gains proficiency in armor, they can cast spells in armor. Whether you like it or not, you have to admit that this is a very obvious cause-and-effect, and that more importantly, it's across the board. All spellcasters are hindered this way. Some spellcasters are just proficient in more types of armor than a typical wizard is. So a non-proficient wizard or other spellcaster who wears armor can't cast spells.
Rogues can't sneak attack with weapons that don't have the Finesse or Light properties. Why? It's because they need smaller, more agile weapons to hit that sweet spot they've learned to attack; other weapons simply aren't precise enough. So a rogue can't get sneak attack dice with a greatsword.
Druids don't wear metal armor. Why? I dunno. You can't say it's because they object to metal, since they can use metal weapons. You can't say it's because metal is unnatural, because it's
not. So a druid in metal armor can't... what, again? "Just because" is not an acceptable answer.
So you have this bit of fluff masquerading as rules, despite no reasoning behind it beyond tradition and no penalties for breaking it.