There is indeed no OT on the altar during the TLM, but there is no NT either. This is evidently another substantial difference between the two rites. In the TLM there is only one book on the altar: the missal. This book contains all the prayers of the mass and all the readings in one big volume - very practical!
What is true is that since the post Vatican II revisions it is now standard for the laity to read the first and second readings. However, the involvement of the laity in liturgical matters has had the unfortunate effect of diverting their attention from the mission, proper to their state, of sanctifying the secular sphere.
Not even the Gospels?
What is true is that since the post Vatican II revisions it is now standard for the laity to read the first and second readings
But that's not the point. You are avoiding the question: why are the first 2 readings read by laity, and at least during one (Epistles) everyone is sitting, while the Gospel is read only by the ordianed, while everyone is standing, if all of it is "verbum Domini" the same word of the same God?
However, the involvement of the laity in liturgical matters has had the unfortunate effect of diverting their attention from the mission, proper to their state, of sanctifying the secular sphere.
Your own Church seems to disagree with that. It was, after all, your own Church that implemented those changes. Are you saying the Church is wrong?