Group in which every p-local subgroup is strongly p-solvable

Definition
Let $$G$$ be a finite group and $$p$$ be an odd prime number. We say that $$G$$ is a group in which every p-local subgroup is p-solvable if every defining ingredient::p-local subgroup of $$G$$ (i.e., the normalizer of any nonidentity $$p$$-subgroup) is a defining ingredient::strongly p-solvable group.

Note that for $$p \ge 5$$, strongly p-solvable is the same as p-solvable, and thus this group property coincides with group in which every p-local subgroup is p-solvable. For $$p = 3$$, it includes p-solvability along with avoiding SL(2,3) among its subquotients. For $$p = 2$$, the notion is not defined or considered.