[RedDevil]

Even if you don't delete the alternator you can benefit from a small solar panel.

Suppose your car battery would lose its charge in a month of disuse.
If it is a 50 Ah battery it will lose 600 Wh per month, so 7.2 kWh a year.
A 5W panel would be enough to provide that, except in the winter months. Step it up to 10W and you will probably never run the battery down.

Now for cost. You do not get the kWhs from the mains but by burning gas to turn the alternator. You need almost a quarter gallon (or 80% of a liter) to generate one kWh, assuming 15% overall efficiency. A solar panel can potentially save you about $6 (or, over here, 12€) per year. You'd earn that panel back pretty quickly.
On another note, because it keeps the battery topped off that will last longer.

So, any drawbacks? There is the panel weight; a tiny reduction on economy and performance. If you mount it outside there may be extra aerodynamic drag (I am looking at mounting a flexible panel ahead of the windscreen wipers). You have to safely hook it up to the battery and unplug it whenever it gets serviced.

I was looking into having a solar panel hooked up to the front window de-icing vent to keep it cool in warm weather. But it can double as a battery top-off when it is cooler.