Rice contains a lot of starch and it is excluded from the GAPS diet for reasons related to gut health and the specific goals of the diet.
This is why:

Carbohydrate Complexity:
The GAPS diet focuses on easily digestible foods to allow the gut lining to heal.
Even though rice doesn’t contain gluten, it’s a complex carbohydrate that can be difficult for a damaged gut to break down, especially in the initial stages of the diet.
The GAPS diet prioritises simple sugars and easily digestible carbohydrates from vegetables and fruits in the early stages.

Gut Flora Imbalance:
The GAPS diet aims to restore a healthy balance of gut bacteria.
Complex carbohydrates like rice can feed harmful bacteria and yeast in the gut, contributing to dysbiosis.
The diet emphasises foods that support the growth of beneficial bacteria, such as fermented foods and non-starchy vegetables.

Starch Content:
Starches, in general, are restricted on the GAPS diet, especially in the introductory phases.
Rice, even though gluten-free, is a starchy grain.
The starches that rice contains, can feed unwanted bacteria in the gut.

Focus on Nutrient Density:
The GAPS diet prioritises nutrient-dense foods that provide essential vitamins and minerals for gut healing.
While rice provides some nutrients, it’s not considered as nutrient-dense as the foods emphasied in the GAPS diet, such as bone broth, meats, and vegetables.
In essence, the GAPS diet is designed to be very restrictive in the beginning to allow the gut to heal. Even though rice is gluten free, it is still excluded due to its starch content, and the desire to remove as many harder to digest foods as possible, in order to allow the gut to heal.