You seem to be under the mistaken impression that your paradox is somehow clever or insightful.
That's a great way to begin a post if you want to promote respectful dialogue.
As somebody upthread posted, what if two players both said, "I want to play the shortest halfing in the world!" That desire is perfectly in line with traditional halfling stereotypes, and yet it results in the exactly the same problem: two players have character concepts* that can't both exist.
If that's what you conclude from my comments, then you've misunderstood the problem, as well as the logic behind my example.
D&D measures strength primarily by the stat, and the racial bonus to strength primarily by the stat bonus. This is why we can say that an Elf with 19 strength is probably not the 'strongest Elf in the world' -- because a high level Elf fighter can easily get a 20. There is a clear starting value and math that all characters adhere to, as well as a clear cap (20).
There's no clear starting value or clear cap to how small a Halfling can be. There's no 'point buy' for height. So the situations are not analogous. This is not the central reason behind the 'strongest Halfling' example, but it is significant to note if you are trying to make an argument by analogy. The smallest Halfling might be 2'6", or 2'3", or 1 nanometer. But unless you are tying height to some game mechanics, it won't make any difference, mechanically.. This doesn't have anything to do with racial bonuses. It has no mechanical effect. There are no rules for it. And it makes no difference to gameplay. And thus that isn't really a rules question; it's a fluff question. And finally, if you get right down to it, you would I assume want to treat all players the same, and give both equal opportunity to set their Halfling's height at whatever low point they want. So let them say their Halfling's height is whatever they want. It makes no difference to me, or to the rules.
Stats work differently than height though. They have a mechanical effect. They do involve a rule question. The question behind the example about 'an Elf stronger than any Minotaur' vs. 'a Minotaur stronger than any Elf' is that in a point-buy and stat-bonus system, you have to answer which if any races get the stat bonus, and specifically how much of a + they get. Because if every race gets the same bonus, then no race is different than any other, and you've just eliminated the racial bonus from the game. So, exactly how strong is your Elf? What is his 'racial' strength bonus? Note Morrus didn't want to answer that question, and nobody else arguing his position has either. Is his racial bonus +2 or less? Then he's not stronger than any Minotaur. Is it +3 or more? Then he is stronger than any (starting) Minotaur, but how can you justify giving an Elf a greater 'racial' strength bonus than a Minotaur?
You have to answer that question if you want to answer this objection, because you have to assign a number.
So I'll ask that again: What specific numerical value should the 'Elf stronger than any Minotaur' have as his racial strength bonus?
I can actually give a clear answer: Players who want to play the strongest starting character possible should choose Minotaur as their race, since Minotaurs get a +2 Strength bonus, while Elves do not. Please note this also eliminates for me the 'problem' of the question of what to do when one player wants to play an 'Elf stronger than any Minotaur' and another player wants to play a 'Minotaur stronger than any Elf'. This question is not a problem for me because the answer is clear: Players who want to play the strongest starting character should choose a race that gets a strength bonus.
But the question remains a problem for those who would allow an Elf to be stronger than any Minotaur. What would you have as this Elf's racial stat bonus? Why should a player who chooses a race not known for its strength enjoy a starting strength stat higher than a player who chooses a race that is known for its unusual strength?
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