In primary schools, one will find naturally gifted children from lower socio-economic backgrounds who may not already be in the gifted education programme.
Sometimes, the parents of such children won't even know that their children are good enough to get into RI/RGS. Sometimes, there are fears that they cannot afford to "keep up" or "fit in".
I suggest the relevant authorities consider "outreach programmes" to nurture these natural talents, engage with their families, reassure them of financial support and prepare them for a time at RI/RGS.
Or invite the top boys and girls in each class or school to sit a special test for RI/RGS. Just make sure that this is a test - unlike the Primary School Leaving Examination - for which they cannot be prepped.