First off, a minor terminology nit: "Neutral" is generally used to refer to hue in photography, not tone. A grey card is both "middle grey" and "neutral grey", but for black and white, only the "middle grey" part of it is important.
As for your question, taking a reflected reading off of a grey card is, IMO, perhaps the best way to meter a scene with an in-camera meter, short of moving in close and using your center patch as a "spot" meter (more like "blot" meter, but if you get close enough, it works perfectly fine).
Reading a grey card is effectively the same thing as taking a reading with an incident light meter; just slightly less convenient in practice, IMO. Exposing to make middle grey appear as middle grey makes everything else fall into place roughly where it "should" be for "normal" tonal relationships.
Of course, you must learn to tweak the reading if the luminance range of the scene does not match the desired tonal range of the print, OR if you want something other than "normal" tonal relationships that are where they "should" be.
For instance, in a contrasty situation that you know has a wider luminance range than you can squeeze onto your prints, you would overexpose the grey card reading, and underdevelop (unless you *want* to lose the edges of the grey scale on the print). In a flat situation that you know has a more narrow luminance range than you can print on your paper, you would underexpose the grey card, and overdevelop (unless you *want* that flat look on the print).
Even when I use the zone system, I always take incident readings as well. It helps me learn to judge the luminance range of various situations, both as a double check, and as a curiosity and learning tool; so I get practice learning how to tweak incident meter readings for future occasions in which the incident meter is all I am using. Surprisingly enough, it is pretty obvious what you need to do after using a spot meter combined with an incident meter for a while, and I find myself using the incident meter combined with educated judgment of luminance range more and more. It is fast easy, and usually close enough to get the print how I want it. Most of all, it is very fast.