The Meaning of Life, the Universe, and Everything.
I don't like this idea for many reasons. Most of the reasons have been said by others, so I won't bother repeating those; but I have one reason that hasn't been stated:
I don't like anything being called/related to bedrock. Because bedrock is super-special; it can never, ever drop, it cannot ever fall as an item. It's a key part of the game, something that exists in the world in certain places, and is the one block that can't be mined in any way at all.
I realise you are not suggesting a recipe using bedrock, but I still dislike the idea because of the association with that special block type.
(I also don't like the idea because of the complexity - having to add 'piercing' to make it balance; it's overpowered but would be frustrating with the slow-down nerf; I can't see any need for it - as it stands, it doesn't make you completely immune, so it's not all that amazing; if it *did* make you completely immune, it would be too OP. And re 'people wanting to use elytra but dying of fall damage' - with diamond ff4 boots, you can fall 40 blocks. At that stage, they really ought to have an ender pearl on the bar to throw anyway)