One color T cell?

They have those, it is an exact match and the T cell engulfs the food. T cells are all about the various ways to digest food in the blood stream. And hey hang around in tissue then take the lymph path back to circulation.  They seem to be a parasite? These pets , constantly nagging for specially cooked food. They are fundamentally different because of the sniff mechanism.

The most natural division of T cell is by the five groups of five, almost dictated by DNA structure, spontaneous. The HC R cells must be made of some combination of the LC cells recombining on a specific surface.  The last LC B cell to exit gets stuck with the long chain antibody which it incorporates.

All they do is digest food and spread the remains all about. Maybe as a way to keep the surrounding tissue well nourished?

White cells evolved from insects:

Hemolymph contains molecules, ions and cells.[7] Regulating chemical exchanges between tissues, hemolymph is encased in the insect body cavity or haemocoel.[6][7]It is transported around the body by combined heart (posterior) and aorta (anterior) pulsations which are located dorsally just under the surface of the body.[2][4][7] It differs from vertebrate blood in that it doesn't contain any red blood cells and therefore is without high oxygen carrying capacity, and is more similar to lymph found in vertebrates.[6

They have no connection to us

The white  blood cell development in the bone marrow seems a convenient cell culture on its own.  For insects, it was an invasion that stuck, a parasite that eats debris. A lot of these antibody clumps go back to the marrow to feed the kids, have no connection to human function.