Let's take your "slash an enemy from 30 ft away" ability.
Zoro from One Piece does this with his various Phoenix Cannon techniques, where he takes a stance, swings, and sends compressed blasts of air to cut the enemy. You are going to tell me "that makes no sense, you can't do that, no one is strong enough or fast enough to do that."
I have also seen a similar technique wear a users Aura/Ki/Life Energy/Soul is compressed and sent through the blade, forming an energy slash. This is also impossible and makes no sense. You cannot compress or manipulate the energy your body produces in anyway, let alone send it out of your own body.
I have also seen a technique where the user swung, and their shadow is what cut the person, becoming solid as they manipulated their shadow. This is impossible and makes no sense. Shadows are simply the absence of light caused by an object blocking that light. They cannot be made solid and hurt someone. Neither could it be possible for a shadow to stab a shadow and use the principle of sympathy to cause a wound on the real person, your shadow being harmed does not harm you.
I have also seen a technique were carving runes and sigils on the blade allows it to shoot blasts of energy. This is impossible and makes no sense. Writing something on a blade cannot cause it to gather energy, especially something that nebulous, let alone release it in a controlled slash, instead of releasing it on every movement of the blade, which would cause constant explosions of energy.
A technique where you psychically extend the concept of a blade or cutting into the mind of the opponent, causing them to bleed? Impossible, blades don't have psyches, and making someone think you cut them when you clearly didn't touch them could not possibly make them bleed.
ALL OF THEM are impossible and make no sense. And yet, every single one of those is a real technique I've seen used in fantasy media, with the real explanation that media gave. None of it makes sense, if you really break it down, because humans can't do these things.... until they can.
The only one you seem to have a problem with is the one where it is pure training, claiming it is impossible because people aren't that strong and they can't train to be that strong. However... the fantasy world doesn't care about that. Zoro's training and strength were on display LONG before he was shown able to send blasts of air. All of the below pictures come from before that moment.
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How do they explain this? Simple. Zoro is really strong. End of explanation. Other people are as strong or stronger than he is in the same world. Why would they need a different explanation? By the time we see him lifting a building we've seen a man made of rubber, a man made of smoke, a man made of sand, giants, a woman who can turn into a mole, a clown that can't be cut and can move his disconnected body parts, a reindeer-man who can shapeshift, a whale whose head it taller than the Eiffel Tower.
No reader ever went "well, I can accept all that, but a man who is really strong? That just isn't possible!" It clearly IS possible, does this mean literally anything is possible? No, the world still has rules it follows. It just doesn't follow the rule that humans are not capable of extreme feats of strength.
So, if gave fighter something like
Impossible Blow: Starting at level 11, as a bonus action you can extend your reach by +30 ft and increase the range of all ranged attacks by +60 ft.
Well... it isn't called out as "supernatural" and so the "how" of the ability is left to the player. You think it has to be magic, cool, your version can be magic. I'll call it a blast of fighting spirit that isn't magical. That works too. An edgy player who is playing a Shadar-Kai and delving into shadow magic might make it them manipulating shadows. That works to. The explanation doesn't matter, because it can be tailored to the character.