I actually think this card would be pretty unbalanced, since there are a lot powerful cards that are not sent to the graveyard when they're destroyed. Certain Eldrazi come to mind. It would probably cost a lot more mana than that, were it an official card.
That card does very little. They way it's currently worded, a trigger goes on the stack whenever the creature is destroyed that sends it to the graveyard. If the creature is in the graveyard when the ability resolves, it does nothing. If it enters the graveyard and then leaves before the trigger resolves, such as a eldrazi or a creature with persist, then the trigger does nothing - If it enters the battlefield again it is considered a new object. Currently, all that it would do currently is make indestructible creatures vulnerable to cards like abrupt decay.
To have it work the way you want, you'd want the following wording:
Cards can't enter the battlefield, hand or library from graveyards.
This shuts down eldrazi shuffle effects, However, it does not stop effects like progenitus - progenitus is a replacement effect for the card going into the graveyard. It never enters the graveyard, so it's immune to graveyard hate.
Of course, an already existing card with a very similar effect is rest in peace, costing just 1W.
Also, "universal enchantment" causes me some grief.