However, if they want to steer into it, I buy in and build upon it. I find it makes the game a lot better. I make sure there are opportunities for them to play up on the trickster elements of a Copper Dragon. I make sure that there are cold based enemies for a Silver Dragon Sorcerer to face. I add homebrew spells to the available list that fit the ematic elements of the breath weapons (including giving metallic inspired sorcerers/dragonborn something that ties to the second breath of the underlying dragon).
For example, I gave a Copper Dragon Sorcerer a 'Boon' after they 'saved'(?) a Temple of Bahamut that allowed them to use spell slots to make a slow cone (30 foot cone for 3rd level slot, 60 foot for 5th level slot, 90 foot for 7th level slot). I also incorporated a staff into that game that does several things including duplicating Copper Dragon Lair actions and Legendary Actions (specifically for Legendary: allowing the Detection, Wing attack, a Tail attack, or casting a spell up to 3 total times per day as a reaction at the end of an opponent's turn as the trigger).
If you want to play one of these Draconic mechanics, I thoroughly encourage you to talk to the DM about how they'll approach it - and if it isn't with gusto and eagerness, I'd save it for a different game later on.
