Grinding NEVER fixes the problem.
All you do is just Kick the Can down the road because you haven't addressed the main issue, the problem under the piece that has sunk. 

It's a Band-aid Temporary fix

When you have a piece of concrete that has sunken down, how does grinding off the good piece fix the bad piece?
Think about it, Let's say you have a brick mailbox and a car knocks a brick out of one side.  Do you knock a brick out of the other side so the sides match or do you fix it?

Grinding is the Most Expensive way to fix.

Year one you Grind.
Year two or three it goes down more and you grind again.
A Year or so later the problem returns because you haven't addressed the main issue. Now you can't grind anymore so you must replace the whole section. You end Paying Triple.

Job Security

Companies that do grinding have Job Security, they KNOW the problem will return in a year or two at the most. For that reason they DON'T warranty their work.

We have numerous examples of issues caused by grinding in the slide show just below.