See, [MENTION=23751]Maxperson[/MENTION], the difference here is 1. I'm not trying to claim that I'm right. I'm simply pointing out the inconsistencies in your claims. and 2. Modelling reality is not my goal. Using D&D to model reality is like nailing jello to a tree. This is not the system for that. And, as I said, waaaay upthread, trying to do so would be far more work than it could possibly be worth it.
You started this with an analogy of using a dagger or a great sword. The problem is, you're conflating two different mechanics. When you attack, you either hit or miss. That is your attack "check". It has no other effect that hit or miss. Just like skill checks or saving throws, it's binary. It doesn't matter how you achieved that success, only that you succeeded.
Now, in combat, we have a second system for determining the effect of a hit. Now, this second system (HP and damage) is not connected to the first system except through critical hits (which don't apply to skill checks). The amount of damage you do is almost totally independent of your attack check. Conversely, your attack check is 100% independent of your damage "check". Now, damage is also given a pretty granular system with HP and the number of checks you have to make in order to kill an opponent. But, again, this is independent of the attack check.
As this relates to skills, it doesn't really track. Skills lack a secondary "effect" mechanic. You roll the check, the lock opens. You roll the check, you climb half your speed. You roll your check, you are X stealthy. There is no effect mechanics. You don't wear down the HP of a difficult lock until it opens. There are lots of systems out there that do have secondary checks for the effectiveness of your skill check, but, D&D isn't one of them.
Now, you want to add, not only a secondary effect to a system that doesn't have them at all, but a secondary effect based on proficiency, which only applies to success checks in all other systems. Proficiency doesn't add damage nor does it make your saving throw better, other than allowing you to pass/fail the check. Having proficiency in Dex saves doesn't mean I take less damage on a successful Dex save vs fireball. I simply take half damage regardless of proficiency.
This is why I keep calling your system inconsistent. It's inconsistent with how proficiency applies in the rest of the game. Remember, we are proficient in both attacks and saving throws. Yet, you're not applying proficiency bonuses in those two systems. Why not? Why only skills?
And there is a second level of inconsistency. Trying to apply proficiency equally to all skills. After all, we don't differentiate the proficiency bonus for different skills, so why is the secondary effect being differentiated? Why do I climb at 1/3 the speed of a proficient climber? And, if I do climb that slow, what exactly does 1/3 of a successful Arcana check actually mean? How much less of a success on a persuasion check can you measure for a trained/untrained check? A trained character makes a perception check to find a secret door. An untrained character makes the same check. They both get the same results - a success. How do you get 1/3 of a secret door?
You are adding a huge amount of complexity to the system, for what benefit? How much better does this actually make the game? You're putting the onus on the DM to be able to consistently come up with ad hoc results on a pretty regular basis, with zero guidance and no real way equivalency. It's just not going to work. You're either going to err on the side of training, thus making it so that untrained characters might as well not even bother making checks (yay, back to 3e skills) or you err on the other side, and now there's no difference at all (yay, 4e skills).
Never minding how you narrate the trained person succeeding with a lower roll than the untrained person, but, still getting a better result. The trained character just succeeds, while the untrained character beats the DC by 5 or so, yet the trained character still climbs at full speed and the untrained character is 1/3 slower? The untrained character still gets less information from an Arcana check? Are we insisting that training means that the character's "minimum damage" for a skill roll is greater than any roll an untrained character can make? Is skill training just that good? How is that believable?