No, it isn't.
The problem is that Shield works that way with anything that improves AC, right? It can combine with anything that improves AC. So Shield is only a good design in a game that doesn't let the caster's AC ever get beyond AC 14 or AC 15. That's not the case.
Meanwhile, Bladesong already doesn't work if you have medium armor, heavy armor, or a shield. So the best you can do is Studded Leather, Barbarian/Monk Unarmored Defense, Sorcerer Draconic Resilience, Lizardfolk Natural Armor, etc. Which are basically just Mage Armor. So the design of Bladesong by itself looks questionable, but in truth it's actually AC 13 + Dex mod + Int mod. Which is a good buff, but it's not that stellar or out of line.
Shield, on the other hand, breaks with anything similar. You can just multiclass Cleric and use heavy armor and use Shield. Even that's not even necessary. If you're a Battlemaster Artificer, you can have full plate and shield very easily, and your subclass-granted Shield spell suddenly takes you to AC 25.