I remember asking once, we don't we just shoot our surplus trash off into the sun and was told that by the cost of launching it outweighs the benefits. Fair!
But what about all of the old satellites and space stations? Why don't we just send a giant magnet around the earth once or twice and then slingshot all that space junk into the sun and thus giving all science fiction writers (when they return from their strike) a plot point they can no longer use in their film scripts?
Seriously though, without the cost of breaching the atmosphere, this seems really cheap to pull, why don't we do this? Why isn't this a standard thing?
The problem with picking up space trash is that it's spread all over in all sorts of orbit. To pick up said trash, the spacecraft will have to alter its own orbit to intercept trash.
The issue isn't so much the size of the thrusters, but the amount of fuel needed. In space, everything coasts along its current orbit, and to go elsewhere you need to expend propellant to alter your orbit. Either by burning loads of fuel in a short amount of time, or with the thrust spread out over a longer burn time.
And when you're finally ready to head into the sun you need to escape earths gravity well, which takes abbunch.
And to hit the sun you will in effect have to burn enough fuel to cancel out the orbit that you inherited from earth to begin with. I don't have the DeltaV numbers in my head, but the fuel cost is immense.