If you increased strength you could carry more and hit things harder.
If you increased speed you got faster.
If you increased endurance you got harder to kill.
Not sure what there is that's tough to understand.
It's not but here's the kicker....
Your weapon skill also determines how much damage you do.
Athletics in the last game determined how fast you ran or swam.
Hit Points determined how hard you were to kill.
And all those play a bigger role then attributes when it comes to determining things.
About the only wild card here is carrying capacity, which isn't tied to any particular skill.
Now, I do agree with those who say that the attribute system was flawed. Start off weak stupid and clumsy and end up might, brilliant, and agile. Not too good. IMHO attributes should be more or less set at character creation and then only rarely increased. That would force the player to decide what their character really is. not a new concept - PnP D&D has been doing it for over 30 years.
And again PnP D&D doesn't use hidden variables it uses simple formulas to determine things. TES games are a little more complicated then that in the formula department, because everything is happening in real time with direct input from the player.
D&D you say your going to attack the goblin, you roll to see if you hit the goblin using a simple comparison formula, then you role your damage using the weapons table damage + strength and enchantment bonuses.
Elder Scrolls game you say I'm going to attack the goblin, the game not only factors whether you hit the goblin, the game asks, did you use a swing or a thrust? How fatigued where you? Did you use a power attack? was the goblin blocking?
Fallout 3, I'm going to shoot the raider, game asks How many rounds are you firing? Is the gun an automatic? What part of the body are you targeting? How good is your skill with the gun in question?
The games calculate this in the amount of time it takes for you to blink.
I'm not saying stats are bad, they give you a general idea of how good a piece of equipment is, or how good you are in a chosen field. But they only give you the general idea at best. So why add another layer here that only adds some minor effects? If Intelligence only effects magic, then why not have the ability to increase the magic pool directly? If Endurance effects hitpoints then why not just go to hitpoints directly and cut out the middleman?