Dragon:Fairy's immunity to dragon makes this match an absolute breeze. Fairy is successfully able to outwall and fairy spam to bring this game to a win.
Outwall, you say? Just because you can't use your STAB doesn't make the game so one sided like you're making it out to be. It's like you've forgotten Dragon has access to some of the best physical bruisers in the tier, and fairy isn't exactly hot on physical defense. It has intimidate Granbull and Mawile, but they can only switch in for drops so many times before they're worn down.
I'll be using Mega Garchomp and Kyurem-B as my example pokemon.
Kyurem handles the mons about the same as MegaChomp, but lacks a boosting move so getting through through the initimidates and reflects can be difficult, but most kyurem go mixed with ice beam and/ or earth power.
252 Atk Mega Garchomp Earthquake vs. 252 HP / 252+ Def Klefki: 306-362 (96.2 - 113.8%) -- 81.3% chance to OHKO (even with Reflect that's a 2HKO, not to mention some MegaChomp variants have Swords Dance to get around this, as well as Intimidate)
0 SpA Kyurem Earth Power vs. 252 HP / 4 SpD Klefki: 182-216 (57.2 - 67.9%) -- guaranteed 2HKO (If Klefki Reflects that makes this a 3HKO, assuming they use Light Screen the next turn, although dual screens will be a pain in the ass while dealing with the other pokemon)
252 Atk Mega Garchomp Stone Edge vs. 252 HP / 0 Def Togekiss: 280-330 (74.8 - 88.2%) -- guaranteed 2HKO after Leftovers recovery (If the Dragon player predicts Toge coming in and lands the Stone Edge, Toge is pretty much screwed.)
252 Atk Kyurem Iron Head vs. 252 HP / 0 Def Togekiss: 182-216 (48.6 - 57.7%) -- 51.6% chance to 2HKO after Leftovers recovery (Iron head is a little more reliable than Stone Edge, not to mention flinches.)
-1 252 Atk Mega Garchomp Earthquake vs. 252 HP / 0 Def Granbull: 169-199 (44 - 51.8%) -- guaranteed 3HKO after Leftovers recovery (Even if you come in you're getting hurt, and Granbull doesn't have the most reliable recovery (lol rest))
-1 252 Atk Kyurem Iron Head vs. 252 HP / 0 Def Granbull: 148-176 (38.5 - 45.8%) -- guaranteed 3HKO after Leftovers recovery
-1 252 Atk Mega Garchomp Earthquake vs. 252 HP / 0 Def Mawile: 306-362 (100.6 - 119%) -- guaranteed OHKO (you're going to need a
bigger boat clean switch for Mawile to dream of coming in.)
0 SpA Kyurem Earth Power vs. 252 HP / 4 SpD Mawile: 260-308 (85.5 - 101.3%) -- 12.5% chance to OHKO
252 Atk Mega Garchomp Earthquake vs. 4 HP / 0 Def Mega Gardevoir: 285-336 (102.5 - 120.8%) -- guaranteed OHKO (Since speed changes don't affect turn 1 of mega, Chomp will outspeed unless Garde is a protect variant.)
252 Atk Kyurem Iron Head vs. 4 HP / 0 Def Mega Gardevoir: 248-294 (89.2 - 105.7%) -- 37.5% chance to OHKO
-1 252 Atk Mega Garchomp Earthquake vs. 252 HP / 0 Def Mega Mawile: 218-260 (71.7 - 85.5%) -- guaranteed 2HKO (Yay, more clean switch need!)
0 SpA Kyurem Earth Power vs. 252 HP / 4 SpD Mega Mawile: 170-200 (55.9 - 65.7%) -- guaranteed 2HKO
0 SpA Mega Garchomp Fire Blast vs. 4 HP / 0 SpD Whimsicott: 236-278 (90 - 106.1%) -- 37.5% chance to OHKO (+2 Earthquake has an 18.8% chance to do the job, it really depends on your set here.)
0 SpA Kyurem Ice Beam vs. 4 HP / 0 SpD Whimsicott: 308-366 (117.5 - 139.6%) -- guaranteed OHKO (ouch)
252 Atk Mega Garchomp Earthquake vs. 252 HP / 0 Def Azumarill: 241-285 (59.6 - 70.5%) -- guaranteed 2HKO (I hope you don't use Belly Drum.)
252 Atk Kyurem Fusion Bolt vs. 252 HP / 0 Def Azumarill: 262-310 (64.8 - 76.7%) -- guaranteed 2HKO
252 Atk Mega Garchomp Earthquake vs. 252 HP / 252+ Def Clefable: 177-208 (44.9 - 52.7%) -- guaranteed 3HKO after Leftovers recovery (The monster barely gets by with a 3HKO from an unboosted Chomp with max defense)
252 Atk Kyurem Iron Head vs. 252 HP / 252+ Def Clefable: 154-182 (39 - 46.1%) -- guaranteed 3HKO after Leftovers recovery
So what you're seeing here is that Mega Garchomp and Kyurem can 1-2HKO the common fairy mons, and MegaChomp barely misses a 2HKO on invested Granbull and Clef, which means if they don't have that investment it's a 2HKO, and Chomp will outspeed, meaning they'll probably lose if they don't have a safe switch.
Another common theme we see here is a lot of Fairies need a safe switch lest they be nailed by the appropriate coverage move and get destroyed the next turn.
Garchomp and Kyurem being able to reliably O-2HKO most fairies makes for a huge strain on the fairy user, especially if Chomp packs Swords Dance, which, if you've boosted prior to the intimidator coming in, makes for a nice easy OHKO, and bumps all the aforementioned 2HKOs in the calcs to OHKOs. Whimsicott is your best bet for stopping SD Chomp, although Chomp has teammates like Goodra and Kyurem to deal with it.
Speaking of Goodra, honorable mention goes out to it as it has access to super effective coverage on every single fairy with Sludge Bomb/Wave and Flamethrower, which does solid damage and avoids Intimidates.
Your Fairy STAB may be a problem, but you can always remember Dragon has things to sack too (Hydreigon is pretty useless without Flash Cannon,) so you'll be on your toes when that -1 Kyurem comes back in all renewed and takes the dog tags of your Granbull.
Now, I'm not saying Fairy has no chance here (as it most certainly does, I've lost to many a fairy team,) you made it out to be a one-sided battle. If anything, this is a neutral matchup, if not in Dragon's favor due to overpreparation for fairies (I've seen a lot of dragons running Poison Jab/Iron Head,) though arguably that's gimmicky and shouldn't be considered.
tl;dr Dragon has sufficient power to muscle through a fairy team even WITHOUT it's lovely Scarf Outrages.