You don't need a gray card anymore with a modern camera. There were two things going on with the standard 18% gray card.
First, it was a shade of gray, so could be used for color balancing. Back in the wet silver days, you could pick only one shade to match between the real world and a print. 18% gray was a good choice for that. You can think of it being sortof in the "middle" of the conceptual color space (remember that humans perceive light lograrithmically, and the film and paper weren't linear either),
Full white is easier to make neutral, and provides color balance too. However, that could either saturate the emulsions (negative) or form so little density (positive) that it wasn't a good way to measure color in the result. Also it was at one corner of the perceptual color space. Even if you got the shade of white right in the final result, other shades could be off considerably due to the non-linearities of the process.
The second purpose of a 18% gray card was for adjusting exposure. Again, that is near the middle of the conceptual gray scale, and was supposedly the reflectance of a average scene. By adjusting exposure so that the response to 18% gray ended up near the middle of the film's response, you didn't bury the shadows or clip the highlights too much.
Nowadays, we have built in exposure meters, so a gray card isn't necessary for measuring exposure. Electronic sensors have a linear response to light level, so balancing the colors can be done anywhwere on the linear scale and the rest will be correct. In that case, we might as well use white, since that is usually easily available and we can see for ourselves that a white object is pretty much white. The more overall incident light a material reflects, the less opportunity there is for reflecting it differently accross the spectrum.
I have measured several digital cameras, and all the ones I have measured have been quite linear from light intensity in to raw sensor value out. There will be some variations between sensors, but the relative sensitivity of red, green, and blue remains fixed for any one sensor. As a result, you can measure it once for each known repeatable lighting condition and compute the color correction for that lighting for that camera once. For example, I have measured my camera with a white target in full sunlight and found the relative response of the sensor to be .5406, 1, .6954. I then use this for color balance without requiring further measurement on any picture I know was taken in full sunlight.
This is to explain why you may still see gray cards and separate light meters used in some circumstances by professional photographers.
A separate light meter is usually used for measuring different points of a scene that are in different locations, oriented differently so therefore illuminated by different lights, or are a different color. This is not so much about setting the overall exposure as balancing the lighting accross a scene.
To measure just the lighting at different locations and orientations, you need some sort of standard diffuse reflecting surface. With today's linear sensors, that can be something white. However, photographers that have been around for a while probably got used to using gray cards for this. They continue to use them because they still work (even though white would now work too) and because they are used to interpreting the result from gray. There is nothing wrong with that, and no reason to introduce something that may cause you to make a mistake because you're used to something else.
However, I still stand by my answer that you don't need a gray card today. Anyone asking this question here wouldn't have 20 years of professional studio photography and using gray cards behind them.