"Old age smartass attitude on."
I used the Zone system as proposed by AA for over twenty years. I have to admit that I got some pretty decent prints using it. However, I have found that my exposures and the resulting prints are much better since I have gotten away from all of the spot metering, previsualization and accompanying mental gyrations, and gone to incident metering. Do I previsualize the zones any longer? Nope. Do I worry about whether I will have a perfect Zone II, III or IV for shadows? Nope. Do I have the tonal values that I want on my prints without all of the thinking? Yes, I sure do. Of course at my age, please understand, that I have a somewhat smaller supply of brain cells left then originally supplied and I damned sure don't want to wear them out by using them unduly.
Incident metering (using BTZS principles) does in fact work better in my experience then the Zone System. While the Zone System, as promulgated, is based on reflective light readings, there are other ways to get better results then the Zone System (again in my experience).
Now back to the original question that the originator posed...is it possible to practice the Zone System without a spot meter and additional backs? The Zone System as it is written?...NO (This will change my original response)
Can equal or better results be obtained without the spot metering, additional backs, and mental gyrations? Yes
"Old age smartass attitude off."