No, false. A normal activity (e.g. jumping) with impossible results is supernatural.
Impossible is contextual. Physically impossible by the standards of modern bio-mechanics & physics is very different from impossible in a mythic or fantasy context, even before supernatural agency comes into it. It's impossible for a RL world high-jump record holder to clear a castle wall. It wasn't impossible for heroes of legend, because the people telling their tall tales weren't being fact-checked by Guinness, it was just a way of illustrating that the hero could really jump.
I don't know exactly where the line is between "improbable" and "impossible" but I know jumping over a castle wall is on the impossible side, and therefore if a human does it (without technology support) it's supernatural/magical. (We can do some F=ma and dy = vo*t + 0.5at^2 if you want to...).
I don't want to, no. Impossible for an unaided human IRL is fine & fairly easily established, it's just not relevant to whether something is supernatural in an imaginary fantasy world - it might draw a relatively hypothetical line between the mundane, RL-realistic and the superhuman, fantasy-heroic, though.
Let alone relevant to a fantasy RPG system where some things are explicitly called out as magical and others not.
"The existence of twilight does not disprove the difference between Day and Night."
That's how I'm seeing you argue against the distinction between super-human and super-natural that I'm pointing out. You're insisting that because something accomplishes the impossible (twilight) that there is no distinction between the superhuman (day) and the supernatural (night).
I disagree (unless I am misunderstanding you), my group is all blasters at heart, they almost never use support/buff/nerf spells (no cleric or paladin and almost always chose damage spells) and the game works fine.
Nod. I'm sure it's possible to run for a group like that in 5e - anything's possible, really, with the amount of latitude the DM has - I just don't consider it too well supported. 5e's fast-combat tuning tends to make offense-heavy parties just roll over many encounters without apparent challenge - the 'too easy' complaint we hear so often - ratchet it up enough to create a sense of challenge and it can tilt over the edge into a death-spiral and even TPK. The support/buff/heal (traditional Cleric) role acts as a sort of net to catch the party when that happens, so lacking it is an issue.
The DM can always be the net, though.
By increase HD healing I was also including he possibility of adding in combat HD healing...Now, the lack of base non-magic classes would be an issue. But that is not, IMO, an issue with the core design. You just need to add more non-magic class / subclass options.
I think we're closer to being in agreement than I thought: yes, the basic design is not, in itself, an impediment to adding and modding enough to make it work for a low-/no- magic party.
Similarly, the basic design is no impediment to just adding Templates onto 5e. But, the existing classes are, since they're not so generic nor so consistent in their design as the idea might need to work well....