In Rabbi Sacks introduction to the Koren Sacks Siddur he writes about two forms of religious worship: prayer and sacrifice.
The prayers in Tanakh were individual and had no fixed formula, time or place.
Sacrifice is by contrast highly defined i.e. what offerings are made by whom and when.
The loss of the Temple resulted in regular gatherings for study and prayer.
Sacrifice went together with the intention of the heart. When the sacrifice was no longer possible, prayer expressed the intention of the heart. That's the meaning of the words of Hosea. Those prayers have fixed times.
But the earlier form of prayer as in the Tanakh remains in place. (And one can and should pray for one's specific needs in one's own way in addition to the fixed prayers.)
So all prayers do not replace offerings.