Teachers would find more gifted pupils if they looked harder. I am aware of 2 children at 2 different schools where teachers denied unusual ability and trotted out the same lines as pretexts for inaction: In both cases, Subsequent standardised testing showed the child in question to be in the top 0.1% / working beyond the ceiling of the test.
Given that I heard the same excuses in several schools, a translation guide to the standard lines they trotted out may be helpful:
"We have five or six children working at X's level" -> we are giving 5 or 6 children the same work because it hasn't occurred to us that some of them might be capable of much more.
"All of our children are gifted" -> we prefer fiction to non-fiction, and are better at creative writing than maths.
"We are an academic school" -> we are a complacent school. We selected on the way in, so we know decent grades are in the bag for the cohort. Let's take it easy and do one-size-fits-all rather than trying to add value.
"He's not the fastest in the class" -> we are so ignorant that we think processing speed / handwriting speed are good measures of abstract/mathematical reasoning ability.
"He makes careless errors" -> he's bored and disengaged. He might actually score higher if we gave him something more challenging, but we think the way to handle this is to give him more of the same banal crap.
"He's not getting 100%" -> We believe in dual standards: other pupils do not get 100% before proceeding to harder material, but for him we shall make a special exception.
"He has to sit through the same class as the others" -> it has not occurred to us to explore options such as acceleration or computer instruction, because we are untrained and poorly read in gifted education
"We can't teach above the national curriculum" -> we either haven't read or haven't understood the national curriculum guidance doc, which is clear that student can be moved to higher levels. So we need to work on our reading and comprehension skills.
"He doesn't show his work" -> He doesn't need to do written work because the questions are far too simple. We could give him something sufficiently complex that he might need to do some written work (and thereby see the point of it), but we think it's much more important to win a pissing contest with a 6 year old / his parents by giving him more of the same, piled higher.