Does "one of the only" actually mean anything?
In my experience it's a way of indicating how extremely rare the 'thing' is.
To use your example of "One of the only people to" ... vs "One of the few people to...". Both phrases indicate that more than one person did the 'thing' but that not many people did the 'thing'.
Using the former phrase is a way to add emphasis and an indication of the level of difficulty or challenge associated with the 'thing'. For example I would use the following in conversation:
"He is one of the only men to land on the moon" vs "He is one of the few people to orbit the earth"
Landing on the moon is much more rare, and difficult, than orbiting the earth. Of course, orbiting the earth is still rare, and difficult.
My opinion or interpretation - don't think you'll find a definitive answer.
Regards
There is denotation and connotation of words in English, and that fact can't be ignored for purposes of logic or argument. Only does not carry a vague implication of a small number. It carries a connotation of a small number, sometimes one alone; an only child, the only redhead, the one and only.
Only: "being the single one or the relatively few of the kind; having no sibling or no sibling of the same sex; single in superiority or distinction; unique; the best."
If it were a vaguely smaller number, then a sentence like this would make sense:
We started with 2,000 tickets, but we only sold 1,994.
Someone hearing that would think the speaker was very, very ungrateful for their very good fortune. It is much more appropriate to say
We started with 2,000 tickets, and we only have 6 left!
"He is one of the only people to do this" - doesn't seem to say anything at all. He's not the only one, but there is no clue whether 3 people have done it or 3 million.
You're right; there is no specific number which constitutes only. In this case, it carries the connotation of a relative few. If it is being used correctly, it does, indeed, mean a relatively few people. Though few, I agree, sounds good.
Thousands of people climb mountains every year, but only 350 or so people have climbed the Seven Summits (the highest mountains on each of the seven continents). Fewer still have climbed the Seven Second Summits (many are harder to climb that the highest). Therefore if someone said, he is one of the only people to have climbed the Seven Seconds", it means something.
The Milky Way Galaxy is enormous, but it contains only ~300,000,000,000 stars. 300 billion sounds like a lot. Seeing as there are 100 billion galaxies in the universe, it's safe to say only 300,000,000,000 stars. Because the Universe is estimated to have about 10,000,000,000,000,000,000,000,000 stars. If my math is correct, for every star in our galaxy, there are ~33,333,333,333,333 other stars. And only about 5000 of them are visible to the human eye.