When you say it's overheating is the gauge up to the red zone on the gauge or is it just above the normal reading? If it is not up to the red zone and is not blowing coolant out it isn't overheating. It's normal for most vehicles to run a little hotter at idle, it's also normal for them to cool down when the engine is speeded up because more coolant is circulating. The thermostat controls the lowest oprating temperatue and unless defective, removing it will not correct overheating. If you really think it's overheating use a cooking thermometer and see what the actual temperature is at idle. I have never heard of a water pump wearing out the impeller blades. I don't think replacing it will help. It doesn't sound like you have a problem unless it really is getting up to or near the red zone. BTW, most modern gauges move in segements rather than showing actual temperature. It may take 10-15 degrees change to cause it to move and the movement will be enough to really notice. If it really is overheating I wouldn't rule out the fan clutch. A fan clutch can cause the fan to lose rpms as it ages.
Clifton