When we translate Tzedokoh as charity, it may be less than 100% accurate. There are many charitable causes. These include Tzedokoh la’aniyim, basically alms to the poor, and Hachzokas HaTorah. They are not the same, and one does not fulfill one responsibility with the other (although there can be overlap). For instance, the tzedokoh that is to be given prior to tefilo is clearly stated as ???? ????? ????, which is for the poor. Likewise, ????? ???????? on Purim is NOT fulfilled with even the most generous donations to yeshivos and chesed organizations.
The needs of yeshivos have never been greater, with multiple sources of funding (government programs and many of the large donors) being severely limited. The current situation for many is desperate. But this is not the same as the obligations for the poor.