Welcome!

Quote
They apparently allow individual children to take math with a higher grade when necessary, but I was told that right now there is only one child out of grades 1-5 who is considered to need this. (Meanwhile, in my child's grade alone there are several children I know that are way beyond grade level in math and could benefit from a more advanced curriculum).
As a next step, you may wish to find out what the identification/qualification criteria are, for this advanced math placement at your child's school.

Quote
Is IB really so inflexible?
There is nothing in your post which suggests that IB is inflexible. While the school formerly separated kids into different math classes based on their levels, but no longer does so (before 6th grade), and now offers 30 minutes of enrichment per week, some may say this sounds like the experience in most schools. The fact that they have one child currently accelerated in math shows they have precedent. You may wish to learn the process. Most parents wish the process of identification/qualification for accelerated placement or advanced academics occurred "automatically" however most parents quickly learn that advocacy is needed because the process is not automatic.

You may wish to read up on successful advocacy approaches so you don't end up smacking the oobleck with a spoon, creating an unyielding solid.