Regarding your first sentence about measurements, it's exactly that a measurement. When a player runs a 4.4 40 at the combine they train weeks and months to get to their peak speed. They run the same drill over, and over slowly trimming down their time. But guess what, it's never exactly the same. It's almost impossible in the real world for a player to run a 4.4 40 consistently. Not to mention that doesn't take into account field conditions, weather conditions, and pads. That 4.4 40 is a number so that you can say "X player is this fast" and the other person will understand that measurement because he understands numbers. If you say "X player is as fast two birds in flight" nobody will know what you're talking about.
Indeed that dash speed is just a measurement. it's also descriptive of said person's "speed attribute", since 40 yards in 4.4 seconds isn't something everybody can attain. Of course it's under optimal conditions. So what? He'll be slower under realistic conditions but he's still going to outrun someone like me, who could maybe some day reach 7 seconds.
As for the reflection of attributes in perks I don't believe there are any attributes reflected in the perks. What you have is a melting pot where strength meets 1h or 2h handed skills. Or where destruction meets willpower/intelligence. The perks a combination of skills and attributes from prior games.
Right. A melting pot. Which means you're trying to make characters that have strength when using a 1H weapon but no strength whatsoever when using a giant hammer. You want to tell me how that makes any damn sense whatsoever? You want to tell me how it makes sense that a warrior with fully perked 1H and 2H but few points in stamina is stupidly strong when swinging a hammer but can actually lift less than a spaghetti-thin pickpocket with the extra pockets perk?
That's the problem. It doesn't make sense. All actors in the game world, and really all people, have a strength attribute. It may seem artificial to put a number on it but we do have such an attribute, and it defines a fair number of things for us. How well we climb up a rope, how well we lift things, how hard we can swing a big hammer (if at all), and so on. Those synnergies would seem natural and once you realise this, not having those synnergies makes a game feel terribly artificial. You may like the fluidity of the gameplay more, but the world becomes much less sensible.
All I'm going to say is that they both lead to the same result. They both represent a character in different ways. With games coming this far I see now reason that numbers have to be the sole determinant on whether I'll hit a person, or not.
Depends on what game you're trying to play. If you want to "be" your character then obviously the character's abilities should matter more than your abilities. If you're trying to play flexible action game with many routes to the same goal then obviously player actions should matter more.
How fast I can run, or how high I can jump. It to me feels boring, cheap, and dated.
Dated? It feels dated that there's a remotely reasonable and detailed model behind the character you're trying to create? It sounds to me like you don't actually want to role-play your character as much as you want a better and more in-depth action game. No offense.
You no longer see XP jump out of some ones body, you no longer even have XP in Skyrim (at least not that I've seen). The question now is do I want attributes to be bars? To me that looks sleeker and more modern. But it still is the exact same thing as number, all of these are just different ways to represent an abstraction. I prefer the more organic form, naked form of representation... just the abstraction itself.
Uhm, yeah. First of all, there is experience in the game. Very much so, as it happens. Every skill you have gets various amounts of experience from certain actions and requires an continously increasing amount of experience to level up. You can't see the specifics but it happens, behind the scene. Every time a skill levels up, it provides experience to your character level equal to that of the new skill level. Character levels are defined as a base of 75 + 25 * old skill level. So, to get to level 2, you need 75 + 25 * 1 experience, meaning 100 XP. If you bring up five skills from 19 to 20 then you get exactly 100 XP and so you level up. It's all there, it's all numbers, but you only get to see a vague representation of it.
Next, you say you prefer a more organic form. Great, I don't really mind, as long as the attributes are actually there. What BGS did was remove attributes that ought to be there and simply worked around with completely idiotic "melting pot" perks and derived stats, resulting in a character model that doesn't make sense and feels utterly fake to anyone who actually cares to think about it.
I can make a character in The Sims or in an FO game or in a D&D game and I can identify with those characters because they feel like abstracted humans, to some extent. I can't do the same in Skyrim because those characters inevitably feel fake. When getting my 1H skill to 80 by killing 783 enemies in melee combat did little to improve the damage I do with a mace, while perk points from enchanting a ton of different items do a whole lot, it feels like I'm playing Diablo 2 and investing skill points. As much fun as D2 was, I definitely wasn't RP'ing in it.

You can hide numbers infinitely, it's called not knowing them. There is no such thing as number for they're just a concept we have created to explain the world. Without numbers there would be no society, no understanding of the world (at least not in the way we see it today), we'd be caveman basically. I understand that, however no matter what there is always something behind the numbers. Do I want the numerical value for what this keyboard weighs? Or do I want to hold it and weigh it with my senses? Either way you're effectively doing the same act, just with different means.
You can hide numbers, but they're still there. But the thing is, I'm not asking for the numbers per se. I'm simply asking for what they represent to be there. You can represent the weight of your keyboard in grams or stones or pounds, or simply as a feeling of how heavy it is, but it still has a weight. And whether you can lift that weight depends on your muscles. You and I can, but starve away our muscles and we'd lose that ability.
I can strap a 40 lb backpack on my back no problem, but my 57 year old mother can barely lift it and my 80 year old grandmother can't lift it at all. When I ask you why I can lift and carry around what they can't, your answer is ultimately going to be that I'm stronger. I'm stronger for a number of reasons, of course, but I AM STRONGER. That's real life for you. In real life person A can be stronger or weaker than person B. The same isn't true in Skyrim, because there is no strength at all. That really old bugger of an enchanter in Winterhold is essentially just as "strong" as Ulfric or any of the warriors in the game, because neither of them have any actual strength.