Summary: X was to be Y is a kind of stylistic 'prediction' made from the perspective of a certain point in the past, predicting that 'X is Y' would happen. John was less than 18 years old already at the time of prediction, and it doesn't really make sense to predict that something will be true that is already the case. That's probably why the sentence is slightly off.
I suspect the first example is a mutation of this:
Some people knew at the time that Anne Frank was not to be sent back to Amsterdam from Bergen-Belsen.
It focuses on a certain point in time and looks ahead. It does so in a generalising or predicting way: "it was not to be".
The use of to [infinitive] after a noun or a form of be contains an inherent, ambiguous sense of prediction or imperative, i.e. an epistemic or deontic modality (see below). In this case, to [verb] indicates a prediction.
The landing is to commence at 18.00 hours. – (Equivalent to the landing shall commence: both a command and a prediction.)
The landing is to be aborted immediately. – (More like a command.)
The landing was to be aborted soon after. – (Equivalent to the landing would be aborted soon after: a "prediction", looking ahead from a point in the past.)
I suspect that the modality of this kind of to be usually tends towards an epistemic modality if it is about the past, "predicting from the past", rather than a deontic modality. For a writer cannot command that something should happen in the past.
So what does this mean? If you are making a prediction, the thing predicted should not be true already at the time of prediction, or it wouldn't be a prediction.
The Franks were distraught when Holland surrendered to Germany in 1940 and they realised that the occupation had begun. Amsterdam was to remain occupied by the Nazis for five more years.
Here the "occupied" part was already true at the time of prediction; however, the whole prediction is to remain occupied for five more years, and that wasn't true in 1940 yet.
To return to the original example number 2:
Q2: Why was only John refused entry?
A2: Because he was the only one to be less than 18 years old.
John was less than 18 years old already at the time of prediction, so what was it that was predicted, exactly? It doesn't really make sense to predict that something will be true that is already the case (and that is not supposed to change within the period of prediction). That is, in my opinion, why this sentence is slightly off.
Example 1 does not have this problem:
Q1: Why was John annoyed?
A1: Because he was the only one to be refused entry to the pub.
At the time of prediction, which is presumably when he was refused entry, we did not know for sure yet that he would remain the only one who was refused, for the next person could in theory be refused as well; but we, the writer, predict with confidence that he shall remain the only one refused within the given period. (Note that the relevant period may even extend to a starting point before the time of prediction.) This confidence may either be a reflexion of John's thoughts or those of his friends at the time, or of the writer's knowledge in hindsight.
I suspect that the second, problematic example is short for something else, which explains why some people would use to be with less than 18 despite the objections outlined above:
Q2: Why was only John refused entry?
A2: Because he was the only one to be less than 18 years old.
A2 (variant): Because he was the only one to [try and enter] under 18 years old.
The elements in square brackets are left out in casual speech/writing. That way, entry does not need to be repeated as enter (although I don't know to what extent that influences this construction). The result is that the prediction inherent in this (special) use of to [verb] is semantically invalidated, as explained above. That is probably what makes it slightly jarring.
Q2: Why was only John refused entry?
A2: Because he was the only one to be less than 18 years old [by August 31 – for the pub allowed minors to enter if they were to turn 18 that same month, out of leniency, despite the risk of a fine].
This (somewhat contrived) variation removes the jarring aspect of the original, in my opinion. It changes the meaning of the sentence entirely, but it does not change its syntax, which I think supports my position that the issue is semantic, not syntactic.
About the fuzzy boundary between truth and desirability:
Why do we say “was supposed to” for “should have”?
