wat.
The Protection Fighting Style does exactly that?
The Interception Fighting Style kind of does this.
Goading Attack from Battle Master does exactly that.
Menacing Attack from Battle Master does this - but with extra steps.
Unwavering Mark from Cavalier does exactly that - and then some...Is Cavalier the Fighter Subclass OP is wanting to make?
...Hell..."Mark" - it's in the name.
Psi Warrior has Protective Field.
The Rune Knight's Cloud Rune is amazing...Not to mention Runic Shield.
Again... wat.
...I think the main problem with 5e, is that "Protecting Your Allies" is simply a "suboptimal" way to play the game. Protecting your allies isn't worth doing. At least; The best way to protect your allies is to kill the hostile. Do more damage. Worry about healing later.