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?