No, one worships graves with exceptions of a few Jahils. You need to do some reading about Sufism, you've got it all wrong [Please avoid Wikipedia].
There is always a chance... if you happen to visit Pakistani rural areas, you will be astonished to see that most of them are equivalent to idol worshipper.
It is duty of the head of state to eradicate any causes of misinterpretation of pure Islam.
I like to quote one of real life case from last govt. time.
Musharraf regime decided to build a rain water lake in one part of Punjab, and there comes an unknown tomb in the middle!
Guess what.... out of no where, Malangs came out and protested against the project... until govt. offer to relocate shrine on higher lands.
I visited the lake this year and found that relocated Tomb, is full of hanging clothes and money pockets are being placed every where, while there is no dead body buried under. Its nothing but pure stone!
Do you really believe that a shrine was built every time a Sufi died? or what ever you call holy!
Tell me one thing, Is it by accident that only Pakistan is blessed by holy men? Is it by accident that large Mosques are being built on shrines? why not people worship the monuments built for Shuhadas?
We need to learn to respect living beings more to keep the Almighty happy.
Adding smiles to the faces of needy is true spirit of Islam.