Do you want to talk about a modus operandi? How about the fact virtually every major villain of this franchise is a mage or was influenced by one? Solas, Corypheus causing the Blight which caused Red Lyrium, Khedra.
Now this is an interesting claim. let's see how much truth there is for that actually. For science:
Major non-Mage villains:
King Meghren (Big Bad of The stolen Throne novel)
Majorlaine and Reileigh (Big bads of the Lelianas song DLC),
Loghain and Howe (Secondary antagonists of all of DAO and have a higher presence than the actual big bad the archdemon),
Branka (Main villain of the Orzammar arc),
Kolgrim (Main villain of the sacted Ashes plotline) ,
The Arishok and Mother Petriece (Big bads of act 2 of DA2),
Duke Prosper (Big bad of the Mark of the assassin DLC),
Gaspard (Fills the main villain role for The masked empire),
Lord seeker Lambert (Kind of the big bad of Asunder)
The Vidasalla (main villain for Tresspasser)
and the most vile villain of all, the Requisition officier (for giving me infinite quest and those being shittiest quests in the history of Bioware to boot).
As opposed to the major mage villains:
Megherens main mage commander in The stolen Throne,
The Architect (main villain of the Calling novel and sedondary villain of the Awakening Expansion),
Zathrian (main villain of the werewolve questline),
Avernus (Responsible for demon invasion in Wardens peak),
The mother (Big bad of the awakening Expansion),
Corypheus (Big bad of the Legacy DLC and DAI),
The Magister dude that acts as main villain for the comic series,
Calpernia (One of Corypheus second in commands)
Alexius (Main villain in In Hushed Whispers),
Erimond (Secondary villain during the Warden stroyline),
Solas (most likely as main villain of DA4)
and lastly probably Flemeth (as overrarchig villain for the series, though her actual end goal has until now never been revealed).
Plus aditionally there is Abominations that sometimes serve as major villains, who are also kind of mages faults:
Uldred abomination (main villain of the broken circle plot),
Desire demon summoned by Connor in redcliffe (obviously the big bad of Redcliffe)
and the Baroness who is kind of the third antagonist of Awakening.
Mage influenced non-mage villains:
Meredith Stannard (Big Bad of DA2, specifically Act 3 influenced by red lyrium),
Samson (Corypheus other second in command during DAI. Influenced by Corypheus and red lyrium),
Florianne (Main villain of Wicked eyes and Wicked hearts. Influenced by Corypheus)
and the Hakkonite leader who isn't a mage but I'll put him here because his plans involve magic.
Lastly, Major villains that are some sort of magical creatures and are influenced by a mage:
Urthemiel (Big bad of DAO, allegedy only exists because of Corypheus),
Darkspawn (in general as Atagonists of the Back to Ostagar DLC. same as Urthemiel),
The Harvester (Big Bad of Golems of Amgarrak. Created with help from Tevinter mages even thogh the dwarves were the driving force behind that f*ck-up)
Envy (Main villain of Champions of the just. Serves Corypheus),
the Nightmare (Main villain during the Warden stroyline, Helps Corypheus.),
Hakkon (is a spirit turned demon summoned into a Dragon assumedly by a mage)
The Titan ("Villain" of the Descent. Not very villainous but he does cause Havoc due to Corypheus nonsense),
So in conclusion we have 13 major non-mage villains, 15 major mage villains (three of which are abominations), 4 non-mage villains that were "influenced" by mages or magic and 7 major magical creatue-villains that are presumbaly the fault of mages.
And there are obviuosly some cases where non-mages are the ones in charge actually (Mehgrens mage, Avernus initially only acting on command of Sophia Dryden and the dwarves being the ones to start the whole Golem research in the first place). As well as cases like Envy and the Nightmare who would aslo be up to no good without mages around. And Meredith was aweful before the red lyrium and Florianne probably was pretty villainous before supporting Corypheus as well.
But yes about 2/3 of villains are mages or influenced by mages (even though I'm deliberately stretching the "influnced by mages" part very, very thin.) Still leaves 1/3 non-mage villains and I'd personally conclude that "virtually every major villain of this franchise is a mage or was influenced by one" is still somewhat exaggerated.
Edited: Added King Meghren to the list.