After reading all this info, I bought a package of Mr. Clean Magic Eraser® ($5.00 for four pads) to try for my own satisfaction. I had a few house cues sitting right here just waiting... 
First, there is "ATTENTION : Test first on an inconspicuous spot with light pressure to see if surface may scratch. Not recommended for use on surfaces that are polished/glossy, or on finishes that are brushed, satin or dark".
There's also the standard warning to "keep away from children and pets to avoid accidental ingestion."
OK, on to the house cues.
I wet the pad and squeezed out as much water as I could.
The cue came fairly clean with some rubbing.
I wet it again and squeezed out less water. No significant change.
Both times I needed to dry the cue with a separate cloth.
Since I had the cues, I now tried my mixture of Simple Green® diluted with 2 parts water in a spray bottle and a cloth. (I've been using this method for a few years.) Yes Martha, I dried the cues immediately after cleaning them...
Well, the diluted Simple Green® worked at least as well as the Mr. Clean Magic Eraser®. Simple Green cost me about $7.00 for a Gallon jug and I dilute it (already said that...
)
Both products caused the grain to raise slightly due to the water, but I quickly rub the cues dry either way. There has never been any long-term negative effects of using the Simple Green and I would expect none from the Magic Eraser either.
The bottom line is that I think I'll stay with the diluted Simple Green® in the spray bottle. I'm a habit oriented creature. Also, I think it costs less for equal performance.
Troy

First, there is "ATTENTION : Test first on an inconspicuous spot with light pressure to see if surface may scratch. Not recommended for use on surfaces that are polished/glossy, or on finishes that are brushed, satin or dark".
There's also the standard warning to "keep away from children and pets to avoid accidental ingestion."
OK, on to the house cues.
I wet the pad and squeezed out as much water as I could.
The cue came fairly clean with some rubbing.
I wet it again and squeezed out less water. No significant change.
Both times I needed to dry the cue with a separate cloth.
Since I had the cues, I now tried my mixture of Simple Green® diluted with 2 parts water in a spray bottle and a cloth. (I've been using this method for a few years.) Yes Martha, I dried the cues immediately after cleaning them...
Well, the diluted Simple Green® worked at least as well as the Mr. Clean Magic Eraser®. Simple Green cost me about $7.00 for a Gallon jug and I dilute it (already said that...

Both products caused the grain to raise slightly due to the water, but I quickly rub the cues dry either way. There has never been any long-term negative effects of using the Simple Green and I would expect none from the Magic Eraser either.
The bottom line is that I think I'll stay with the diluted Simple Green® in the spray bottle. I'm a habit oriented creature. Also, I think it costs less for equal performance.
Troy