They needn't be removed. Just made invisible. Physics engines and elaborate animations/simulations have made it that so, in theory, you don't need the numbers. An Orc just IS stronger then a Bosmer. From day one he swings harder, moves slower, the whole bit. Altmer cast stronger spells. Khajiit are faster... These things are true of the races without needing attributes.
A Bosmer whose strength has been considerably increased through training, magic, or whatever else may be significantly stronger than any given Orc. Likewise for your other examples. One of the major purposes of any statistic in an RPG is comparison. If attributes can be increased, they serve a purpose, and they can and will differ between individual characters (and monsters).
From there, each one imroves as they level. Endurance can be chosen through stamina, Willpower through Magika. If your character has high intelligence, then solve the puzzles in the game and prove it. As for dialogue, it can be skill driven. Of course a Master Blacksmith has something intelligent to say about blacksmithing.
Morever, all skills filter back into attributes, making them redundant. Swing a sword, get stronger. It's six of one, half dozen of the other.
This seems to be an argument for the removal of all statistics, though - if the Strength attribute can be dissolved into racial characteristics and is unnecessary to gameplay due to player input and ability, then skills are similarly unnecessary. And attributes serve purposes that skills do not, and vice versa; for example, is a character's melee attack the only related function and purpose of his physical strength? Skills represent relatively specific activities which are affected by one or more attributes, but consider the situation in reverse: attributes represent physical and mental capabilities which encompass and affect far more activities than could ever be represented by skills.