In the ASOIAF books, the return of the dragons triggered interesting side effects, namely the spontaneous lighting of obsidian candles at the Citadel, the strengthening of pyromancer spells as mentioned by Pyat Pree, the flaming sword of Beric Dondarrion, the rise of the Lord of Light, to name a few.
Right now, the Targs have a whole stable of dragons - magic should be rampant in this world right now and more prevalent in every day life, ostensibly informing the events in the story. It really isn’t. Things are still too mundane in this world and shouldn’t be, so far of what I’ve seen. Now, admittedly, I’ve only watched the first episode and perhaps there is some magic usage in later episodes that I haven’t seen yet. Somehow I think not.