Why do Boolean modules and dynamic algebras have so many properties that relation algebras lack? I like to think of it in terms of holding the two essential ingredients of dynamic and relation algebras at the proper distance. Too far apart and all you have is a Boolean algebra and a monoid. Too close and they interfere destructively.
Brink [Bri81] argues that Boolean modules are relatively well-behaved compared to relation algebras. I make a similar point in the context of regular algebras versus dynamic algebras [Pra79a,Pra79b,Pra80a]. Redko [Red64] has shown that the equational theory of regular algebras has no finite basis. Conway [Con71] has observed that this theory has a three-element model in which x0 + x1 + … + xn is constant with increasing n > 0 yet x* is not that constant, a discontinuity we refer to as Conway's Leap. Replacing one-sorted regular algebras by two-sorted dynamic algebras disposes of both these aberrations, as we will see later in the section on properties of dynamic algebras.
The common idea here seems to be that intersection and composition in too close proximity only ``fight'' each other. If instead each is moved to an appropriate sort, a logical sort accommodating the Boolean operations and a relative sort for the Kleenean operations, the separation seems to encourage cooperation instead of competition.