You don't grasp the problem. Since it is the DM who decides the exact wideness of the chasm, probably by looking into a list how far it needs to be for a certain check, why go thorough all those hoops and just decide for a check and tell the players that the chasm is a bit too wide to easily jump across.
If one player tells me his character is exceptional at jumping, why should I tell them ah, i see, you can jump exactly 19 ft. But too sad, my chasm is exactly 20 ft across. So your extraordinary ability is not helpful.
In your previous example, you said this:
the chasm is 15 ft wide. My jump distance is only 9ft. Can I try it anyway?
Yes. But it is a hard check
Is that a hard check because you increased the distance by 5 ft [making them short by a foot, but that was reasonable fudging]? Increased it by 10 ft [putting them over the limit]? Or doubled the jump distance [putting them over the limit]?
As a DM, not just as a player, this
MATTERS. Because when I look at a player with a jump distance of 18 ft, I need to know whether or not the chasm is reasonable to jump if it is 22 ft across, 28 ft across, or 38 ft across. Let's say I'm a human champion fighter, and the DM has stated that it is 40 ft gap between the walls and the castle. My jump distance is normally 22 ft, should I even consider that I can jump that distance? If it is a DC 20 check, and I have a +7 with advantage.... that isn't a bad deal, maybe throw a bit of bard inspiration on it. If a DC 20 check can only extend me to 27 ft, this is impossible and I need another solution..
Sure, if the DM is making a chasm, they can decide how hard it is to cross, but unless they have stated their rules the player is probably going to see they can't make the jump with their known numbers, and dismiss the attempt out of hand.
If those examples are useful and have a good range. What I wish for is having some typical applications for a skill listed for each DC:
Lets mak an example:
Athletics:
DC 5: climb a ladder at fast pace, swim in a quiet lake without clothes.
DC 10: swim in a stream, jump on a small table.
And so on.
So instead of making an exhaustive list of tasks with DC's I'd like it to be sorted by DC and some examples so a DM can get a feeling for probabilities... most DM's make every check on step too hard.
Maybe have a big box with an explanation why making checks too hard sucks. How it leads to powergaming and so on.
I don't disagree with your point broadly, but there is an issue. Well, a few issues.
Swimming is never a check, unless you are dealing with rapids or rough seas. I know some people disagree with me, but that is what the book says. So, it is never a roll to swim in a stream or a river... so is swimming through white water rapids a DC 10? That's when the rolling starts, so that would make sense right?
And jumping onto a small table would be the same... except, wait, a person with a +1 strength who can run up can jump onto a 4 ft surface without a check. So, for them, there should be no DC. And are we talking landing on their feet, or grabbing with their hands and pulling up?
This is why, actually, I think we would be better serve with examples and rules in each section. A DC 10 jump might just be "add your strength mod to the distance again, minimum of +1" which makes sense for how the jumping rules are presented, while a DC 10 swim is going to be more about "swimming through strong currents or thick liquids" which makes sense for how those rules are already structured.
I agree, don't want a million tables, but since the rules for these things already work differently, the examples need to be different to make sense.
It is more helpful to adress DC's to checls on the fly based on the felt difficulty. Which is always very circumstantial.
And it is more helpful to teach them not to describe surroundings in exact numbers. Big room, small hall, a wide chasm...
I disagree. Because the felt difficulty is so malleable that it becomes impossible to guess. And the players need to have some conception of how difficult something might be, to consider it.
I've altered the strength lifting rules so that player's feel as strong as I think they should, but if I don't tell the player "your goliath barbarian is strong enough to pick up and throw a Harley" then they aren't going to even consider trying to rip the steel bars from the stone of their prison cell, because they feel that would be too hard for them. They need to have reference points, even vague ones, and so the DM. After all, I imagine you are thinking that should be a DC 20 or 25 check to accomplish, since breaking manacle chains is a DC 20 strength check, but for me, I would actually lower that manacle check, and for a strong enough character, they can just do that task, because I have the basis of how strong they are to reference, and if you can throw a small car, I don't think you are going to reasonably struggle to snap unenchanted chains with a few minutes of effort.