Bladesinger 9 / Eldritch Knight 3

Had an idea to basically make a Duelist style character who was also a decent (if limited) spellcaster. Basically DEX would be the highest stat and the primary weapon would be The Duelists Prerogative, along with Bhaalist Armor for additional damage. With the extra reaction I could reasonably counterspell most dangerous spells. Is my reasoning sound or does this need more workshopping?