The DM in a campaign where I am playing doesn't want to allow Booming Blade opportunity attacks with the Warcaster feat. Fluff-wise reasoning is, with OA there is not enough time to first "brandish the weapon" and then make the attack. Mechanical real reasoning is, the damage of Booming Blade seems just too high, and it works too much like the Sentinel feat against arcane-savvy enemies, while being likely to just outright kill any less smart, wounded enemy, who decides to dash away (without dash, the opponent can usually just follow and attack anyway).
Especially combined with Dissonant Whispers, which my character also has, the numbers do seem crazy: My level 12 PC has potential to do repeatedly 3d6 psychic damage (1st level Dissonant Whispers) + 1d8+1+4 piercing damage (+1 rapier, +4 DEX) + 5d8 thunder damage (Booming blade full damage) by expending just 1st level spell slot, action, and reaction, if target fails a DC 18 saving throw (this is achieved with an item). This is average 42,5 damage even 1-vs-1, and if there are allies there, they get a swing too.
Also the damage upscales nicely with character level, unlike most other opportunity attacks.
A comparable "normal" spell would be Shocking Grasp, which in the above example would do just 3d6 psychic + 3d8 lightning damage, average 24.
So as you can probably guess, I can't honestly say I disagree with the DM, but still it would be a sweet combo, so the question:
What factual arguments can be made to convince us that Booming Blade opportunity attacks are not unbalanced, unreasonably powerful, and completely overshadowing other PC's opportunity attack abilities?
Best Answer
Booming Blade seems to be a spell designed to make spellcasters who like Melee viable with only one attack per turn. It always does a decent chunk of damage and has a movement restriction effect that you're manipulating by using Dissonant Whispers. So that makes a nice combo.
To see if it's unreasonable, it's easiest to compare it to other characters who are powerful with a weapon without getting a ton of attacks; the most obvious comparison being the Rogue.
A level 12 Rogue would deal an extra 6d6 sneak attack damage on their opportunity attack, assuming they get it (which, if this combo is a thing in their party, they surely will). That's an average of 21 extra points of damage on top of their normal hit damage.
It compares pretty favorably to the 22.5 average extra damage that your combo does. And the Rogue spent nothing on it, this is just what Rogues do. You had to get a Feat for it. The Rogue can probably add on more damage if they're willing to use a Feat as well.
The really scary thing here, is Dissonant Whispers in a party with strong single melee attacks; Booming Blade is just an obvious option for it. Using Green Flame Blade does about the same damage, but to two targets. There's plenty of things you can do to amplify opportunity attacks.
Even Eldritch Blast would do about the same damage if you can get around the Disadvantage for being in melee (but that'd take another Feat, so a bit more expensive). It'd deal more with Hex up.
Divine Smite costs a spell slot, but a Paladin's default opportunity attack with a Smite can already deal more damage than you do. And they can use Great Weapon Master if they want to really make it hurt.