No, you do not need all of them.
There are (far) more than needed because that way players can choose which ones they want to get. You can pick them up while going through whichever zones you want to play first rather than having to go out of your way to visit the places which have them and if an individual skyshard or an entire zone is too much trouble you can safely skip it and get them from somewhere else.
I have to admit I don't know if there's enough skill points available to unlock and morph every single skill a character can have, but that's because it's never come up for me. I know there's more than enough to unlocked everything required for multiple builds - for example one character can have all the crafting skills, all their class skills and enough other stuff to swap between 2-3 builds whenever they want without getting all the skyshards in the game.