You can see agility and physical strength, and yes it's painfully obvious. Madden is an example of a game that uses numbers to represent abilities of the players and it can be highly addictive to watch your players progress over time slowly gaining elusiveness, strength, etc. But it doesn't make them feel natural, I never relate a number to speed unless it is in a video game.
So when you're talking about new potential running backs for your favorite football team, you don't talk about how fast he can do a 60 yard dash? When discussing Usain Bolt, you don't talk about his 100 meter sprint time at all? Really?
If we are to describe relatively abstract people inside a fictional world then assigning them attributes is a great way to do so. Mind you, strength doesn't have to be represented in numbers. Putting numbers on attributes is indeed very "specific" and perhaps overly accurate. We could use letters instead or we could make labeled categories. Categories for strength could be: Weaker than your average houseplant, pathetically weak, mush for muscles, weak, average, muscled, strong, can wrestle with oxes, wins when wrestling with oxes, absurdly strong, titanic.
It's not that numbers absolutely have to be used to describe strength but rather that all people have some level of strength that can be described in different ways. If a battle-hardened Nordic warrior arm-wrestles with a Breton librarian then you'd expect the Nord to win. Having that reflected in the game world makes sense. Not having any description of how strong, agile, sturdy, smart, charismatic, strong-willed, well-behaved, fast, and quick-reflexed your character is relative to everybody else does not make it easier for me to relate to my character, in fact it does the opposite.
Of course, if I'm making a Breton librarian who happens to be an arm-wrestling freak then I'd expect to arm-wrestle with the best of them and utterly destroy any other librarians I arm-wrestle with. You could try to make that perk-based but in the best case you'd end up with a five-scale attribute and in the worst case you'd end up with meaningless gunk like what we have in Skyrim, where there's effectively none of the synnergies you'd expect from being a hugely physical warrior or a brainiac mage while the few synnergies present make no sense whatsoever.
I don't necessarily want perks to disappear, but I do want them to be used with reason. That which is an attribute should be described as an attribute and not indirectly with perks. Describing attributes through perks is like referring to cars as wheeled umbrellas with windows, doors, and an engine. It's not sensible, smart, elegant, or clever. It's moronic, confusing, annoying, and a colossal waste of time. Just call it a [censored] car and be done with it.
As for your mage/warrior thing that is true even with attributes. I can make a mage who is just as fast, of not faster than a warrior in Morrowind, attributes don't inhibit that at all.
Indeed you can. And you should be able to do so. You'd then have made a sprinter-mage, which is fairly odd, but maybe he just likes running. Regardless, you'd have to take your time and practice running for you to be able to outrun that warrior. That's totally fair and how things should be. Meanwhile some other mage might have spent the time you used running around on mastering spells a bit more or training to use light armor instead of clothing, which means he's more arrow-resistant than you are, even if he's a lot slower.
And to answer your question a solution would be for weight to make a difference on your characters speed, and jumping ability. If your actual muscle mass affected your damage, and the weight of yourself and your armor slowed you down then you would have a much more organic, natural alternative to reach the same destination as if you had just plain attributes.
And how would the game know how much muscle mass a character has at any given point? Exactly, it would treat the muscle as an attribute. Which takes us back to strength and rate of encumbrance. That's quite like Morrowind, isn't it?
I understand the infinite depth of numbers, and how they can be applied to any situation. However for me I prefer a game with less numbers, not because I don't like numbers, but because for me they bore me, and distance me from my character. I find it hard to relate to my character if he is just the sum of his numbers.
Any character in a software application is by necessity just the sum of his numbers. You can hide the numbers, you can abstract the numbers, but ultimately any character is just a collection of numbers. For instance, you might also describe the perks in an x-dimensional vector, with each dimension corresponding to a specific perk. With attributes gone and skills almost meaningless except for unlocking perks, your character could then reasonably be described as merely some vector.
By removing attributes, you're not getting a numbers-free character, you're merely getting a "sum of his numbers" character based on less numbers, which makes him less interesting and more generic. Now, you're quite correct that all characters could become more or less the same thing in Morrowind, assuming you cared to invest crazy amounts of time. Did you actually care to do that?
I've played Morrowind a whole hell of a lot, I consider myself fairly experienced with the game, and I've never managed to max out a character. Not because it would take too long (training cheese + console...), but because I simply couldn't be bothered. True, I made a fair few characters that could use any weapon or magic to destroy any enemy, but so what? Morrowind wasn't about the end result but rather the journey, and the journey would not be the same for a Breton battle-maiden or an Altmer pure mage.