A school which is genuinely concerned about

[keannu]

When there's no if-clause in conditionals, like if it is replaced only by a noun phrase like "A school which is genuinely concerned about the welfare of its students" followed by "would", is it a real conditional(conditional1) or an unreal conditional(conditional2) or hard to define? Does "A school which is genuinely concerned about the welfare of its students" denote a likely school(predictive, conditional1) or a counterfactual school(conditional2)?
If it refers to a counterfactual one that does not exist, and to the contrary, if you use "will", does it become a predicitve real conditional to mean "there can be such a school"?

ex)For elementary schoolchildren, recess is just as important as science or math class. However, many schools across the nation aren't giving students enough opportunity to play outside. A school which is genuinely concerned about the welfare of its students would understand the importance of recess. Kids learn about teamwork and sportsmanship when they play together. In my opinion, all the tests in the world coudln't teach a child social skills as well as an hour of recess each day.....

[5jj]

I'd write it as " A school which is was genuinely concerned about the welfare of its students would understand the importance of recess.

[keannu]

I'd write it as " A school which is was genuinely concerned about the welfare of its students would understand the importance of recess.

I feel you mean it is a counterfactual present that the writer feels doesn't exist in the world. I got it.
And one more, I'm sorry , The following's "couldn't" seems to mean an unlikely or counterfactual assumption(conditional2), but "all the tests in the world" doesn't seem to denote an impossible thing as we can think of "all the tests", so this may sound a play on words. I can roughly understand what it means, but to analyze it, I need to know it for sure.
What is the difference between "All the tests in the world can't teach..." and "All the tests in the world couldn't teach..." ? I know the former is real while the latter is unreal, but the two are kind of confusing....

ex)all the tests in the world couldn't teach a child social skills as well as an hour of recess each day.

[keannu]

I'm just curious when a noun replaces if-clause, if it means a counterfactual or the noun just designates a certain thing.

a)A superman could lift Empire state building. - A superman is a counterfactual(imaginary) being.
b)Obama could visit Empire State Building this week.- Obama is a real person, not a counterfactual(imaginary) being.
So b is kind of different from a, isn't it?