No and that's a pretty serious misrepresentation because you are trying to use narrative phrasing in a discussion about a mechanical element within the rules. There are already a bunch of spells and abilities that key differently from target to target based on creature type. Here is a partial list of things that already key off creature type in some way: turn undead, divine sense, lay on hands, divine smite, holy nimbus, channel divinity, favored enemy, Pirmeval Awareness, Grim Harvest, Antilife shell, blight, chill touch, command, commune with nature, Cure wounds, detect evil & good, Forbiddance, Hallow, Heal, Healing word, Hold monster, Holy aura, Magic circle, Mass cure wounds, Mass healing word, Phantasmal force, power word heal, Prayer of healing, Protection from evil & good, raise dead, shapechange, Simulacrum, Spare the dying, Sunbeam, sunburst, divine Word, Planar Binding, etc..So, what you are describing is that we must care that elves are Humanoid type Fey Subtype because it is a mechanic, and if the system doesn't build itself to use that mechanic, it will be replaced with what is needed for a better story.
Problem, the things you described DON'T have mechanical implications and NEVER WILL.
No one is EVER going to make DnD Necromancers use different spells or different materials to animate different humanoids based on their subtype. That would be a nightmare. No one at WOTC is going to build out the medicine skill to the degree that the weight of a specific humanoid will be paired in a chart to the proper measure of medicinal powders, let alone make that DIFFERENT for each sub-type.
This is why I think that using the terminology to define the species in this way would never work. No one is going to naturally want to refer to (Humanoid Type, Subtype Fey, Sub-Subtype Elf, Sub-Sub-Subtype Wood) as they are talking, in or out of character. And if the system wants to use these things and force them to matter, then we are going to potentially get these exact things you are talking about that the VAST VAST majority of people will immediately complain about because all it will be is a giant, useless mess.
The fact that this tedious list needed to be assembled to prove that things which have keyed off creature type with mechanical implications for multiple editions illustrates why 5e's efforts to streamline & simplify creature type away elsewhere causes problems. When you apply a question like "is this thing narrative fluff or a mechanical thing?" to what the new term for "race" should be the answer is that it is mechanical & as such mechanical concerns should hold heavy sway over what the term is mechanical.