The "Zone System" can be applied in digital but, as good as sensors are ... it's hardly necessary. I'll concede that knowledge of the "Zone System" may help when configuring your camera in the "manual" mode. But, internal massaging of the data is so far advanced, as are the current sensors (Thank you Sony.), that the range of contrast now available to shooters is, far and away, superior to what the "zone" was developed for. (I'm speaking only to full sized sensor cameras. Only large pixels are capable of capturing sufficient information for enlargements with an extremely wide range of contrast.)
The "Zone System" may be something some wish to take into consideration when preparing to take a static shot but, certainly not a requirement for an exceptional shot in my opinion. I suppose it's simply what one is comfortable with. Still, I'll assert today's sensors, lenses, internal software and post processing software far surpass the "Zone System" except maybe for those conversant with the "system" who may make use of it for reference purposes. I never give it a thought anymore and I've been shooting for 60+ plus years. Ansel simply isn't relevant anymore except for those still using negatives and shooting in black and white. (An opinion only guys. I find the "zone" irrelevant for the type of shooting I do.)
It is, in the end, a personal choice, just another tool to get to the image you desire. It's much easier to expose for what you desire, shadows, highlights or a combination of both and make any necessary adjustments in post.
The American Bald Eagle is a subject I often shoot. The white head and light gathering brown body make this a complicated shot if sufficient detail is to be captured in the two extremes. I can't approach the subject with a reflector to lesson the contrast so, I meter for the head and allow the sensor to capture sufficient detail in the darker, less reflecting body feathers. If I have the detail I can balance in post. (If I "blow out" the highlights I don't have a even a salvageable shot.) They are a tough subject! This is why I set up the camera for the target subject before I leave the house. (This preparation even works sometimes. Don't for get the adage, "The lens desired is usually back in the truck or at the house.")
I'm not addressing video as the OP didn't mention such. I will anyway to assist in explaining my position. Video is, if shooting with serious intent, a totally different can of worms. The end result of a video needs to cover, without too much range, only a moderate amount of contrast. Video, commercial stuff, requires balancing light before the camera is even turned on. Proper video often requires multiple light sources, usually modified with snoots, umbrellas, reflectors, and the like. Extremely technical in my opinion.
I don't shoot commercial video as I really have no interest in such. Jesse is probably the most knowledgeable member when it comes to "movin' pitchers." Maybe he'll chime in. I'm not even sure how much cinema is shot in digital at this time. But, I do know light is severely controlled in commercial videos as blowout" simply isn't tolerated.