It depends onnthe point of view. If you are a citizen of Alabasta, Dressrosa or you suffered by the hands of Doffy, Moria, Croco etc. As a civilainnyou have all the rights and reasons to ask for their demotion, also if things get really dry tou can bet the shikis will turn tail and betray the WG (Boa, Doffy, Croco etc.) also how they were played huge time by BB through the shiki system. There is also the forner admiral Z losing an arm because of a shiki and thus, when he knows this guy is now a shiki, leave the marines disgustes (and if it is non canon). This is also a blow to the rigtheous face of the WG (have pirates work for the WG).
On the other hand now they are declaring war to a former yonko level dude, Mihawk, who for some.miracoulous reason (for the WG) was helping them also while not being a jerk with civilians (it seems Mihawk despises war going by his Rukushina island behavior with the baboons). Now he is no longer an ally but an enemy (they could have done an exception for him but it seems Oda has other plans). And you also turned Boa, Weevil etc from allies into enemies. If tomorrow another yonko attack the marines will this SSG weapon be enough to replace the shiki? And what if the shikis join the attack? It has ti be noted they should also have a good amount of knowledge about the WG given how they could enter and leave a places like Impel down (see Boa bringing in Luffy) or enter Marijoa.