Using Green-Flame Blade, Booming Blade, and Lightning Lure gives these two subclasses much of the feel they need. Both invoke a feeling of characters who use their weapons while slinging spells. So does the Hexblade, the Battle Smith, some Paladins, and some Rangers.
Unlike when the Hexblade and Battle Smith were added to the game, the Bladesinger and Eldritch Knight didn’t get access to spells like Thunderous Smite or Zephyr Strike or Ensnaring Strike. The Smites all fit the two narratives. The Strikes are just the two previously listed and Steel Wind Strike.
A Dungeon Master that adds these ten spells for their players helps that player play a character who fits the mold as a weapon-caster. Giving a PC a few moments a day, because they take spell slots, when that character emphasizes the vibe of the fiction that inspires their character is great. They aren’t stepping on the toes of the Paladin (who has the Smite feature still) or the Ranger (because Favored Foe and Hunter’s Mark are their combat signatures).
Ten spells and your players will be more like the character they want to be, without the need to be a Hexblade sworn to a odd mystical sword, a Paladin sworn to a cause, or a Ranger protecting civilization from the Wildes.
Full Moon Storytelling 