What is the meaning of the zero article for a plural noun phrase in English?
First consider the singular:
“A school allocates places to the pupils who score highest.” This has to be interpreted in context. It can mean
(i) one random example of a school allocates places to the pupils who score highest.
Or
(ii) one example, known to the speaker but not identified, of a school allocates places to the pupils who score highest.
Or
(iii) A school that is representative of all schools will allocate places to the pupils who score highest.”
Could you confirm that “schools” here means “all schools”?
The main problem is not “schools” but “all”
The plural is
“Schools allocate places to the pupils who score highest.”
This has to be interpreted in context. It can mean
(i) All schools allocate places to the pupils who score highest. In which the meaning of “all” varies contextually between “every school in the universe and without exception” to “the two local schools”.
Or
(ii) Generally, all schools allocate places to the pupils who score highest. This concedes that there may be specific exceptions.
Or
(iii) Schools that are representative of all schools will allocate places to the pupils who score highest.”
Could you confirm that “places” here means “some places” ?
No. It is not possible to confirm that at all. That information does not exist in “places”.