Isn't Toshinori pretty much the same as Deku when he was quirkless? If All Might is qualified, then so is Deku.
One punch was all it took Garp to break Chinjao's will and he was a conquerer. Conquerers can work under the other COC users. Destro and Mechia just happened to bow their heads before the superior conquerors just like Katakuri, Rayleigh, Zoro, WB, BM and Kaido.