The Talmud proves that there is no alternative to the proposed resolution.

As, if you do not say so, that the laws of offerings and the laws of prayers are related, it is unclear: According to Rabbi Yosei son of Rabbi Hanina, who instituted the additional prayer? It is not one of the prayers instituted by the patriarchs. Rather, there is no alternative to the aforementioned resolution: According to Rabbi Yosei son of Rabbi Hanina, the prayers were instituted by the patriarchs and the Sages based the times and characteristics of prayer on the laws of the offerings.