"After the homily" or "instead of the homily" reflections drive me nuts!
According to Redemptionis Sacramentum:
“The homily…’should ordinarily be given by the Priest celebrant himself. He may entrust it to a concelebrating Priest or occasionally, according to circumstances, to a Deacon, but never to a layperson.” (no. 64).
“the homily on account of its importance and its nature is reserved to the Priest or Deacon during Mass.” (no. 161)
“The prohibition of the admission of laypersons to preach within the Mass applies also to seminarians, students of theological disciplines, and those who have assumed the function of those known as ‘pastoral assistants’; nor is there to be any exception for any other kind of layperson, or group, or community, or association” (no. 66)
Any such "reflection" should be done after Mass or before, not during. There is an exception “for serious reasons” to include instruction during the Mass “after the Priest has proclaimed the Prayer after Communion,” but it should not become a regular practice. Thus, Redemptionis Sacramentum states:
“If the need arises for the gathered faithful to be given instruction or testimony by a layperson in a Church concerning the Christian life, it is altogether preferable that this be done outside Mass. Nevertheless, for serious reasons it is permissible that this type of instruction or testimony be given after the Priest has proclaimed the Prayer after Communion. This should not become a regular practice, however. Furthermore, these instructions and testimony should not be of such a nature that they could be confused with the homily, nor is it permissible to dispense with the homily on their account.” (no. 74).
“As regards other forms of preaching, if necessity demands it in particular circumstances, or if usefulness suggests it in special cases, lay members of Christ’s faithful may be allowed to preach in a church or in an oratory outside Mass in accordance with the norm of law.” (no. 161)
Are such layperson, acolyte, and/or seminarian homily-like "reflections" common in many parts of the Church? It seems so. But it seems to me an abuse of the liturgical norms worthy of fraternal correction.