While the Roman Rite of the Catholic Church requires a crucifix to be placed either on the altar or near it, there is no specific requirement on the exact placement. It could be placed on the wall, be the processional cross, or simply be a small cross placed flat on the altar.
However, Pope Benedict XVI was a strong advocate for placing a large, visible crucifix on the altar. Pope Francis has continued this tradition as well, following the example of his predecessor.
Benedict XVI explained his reasoning in his book Spirit of the Liturgy, which the Vatican quotes on its website. He first explains the claim that a crucifix on the altar would "obstruct" the congregation's view of the priest.
"It is not necessary in prayer, and more than that, it is not even appropriate to look at one another reciprocally; much less so when receiving Communion. [...] In an exaggerated and misunderstood implementation of 'celebration toward the people,' in fact, the crosses at the center of the altars were removed as a general norm - even in the basilica of St. Peter in Rome - so as to not obstruct the view between the celebrant and the people."
From Benedict XVI's point of view, the crucifix is not an "obstruction," but an "invitation" to look together at the Lord.
"However, the cross on the altar is not an impediment to sight, but rather a common point of reference. It is an 'iconostasi' that remains open, which does not impede being mutually in communion, but is a mediator and still signifies for everyone the image that concentrates and unifies our sight. I dare to propose the thesis that the cross on the altar is not an obstacle, but the preliminary condition for the celebration 'versus populum.' Also made clear with this would be the distinction between the liturgy of the Word and the Eucharistic prayer. Whereas the first is about proclamation and hence of an immediate reciprocal relationship, the second has to do with community adoration in which all of us continue to be under the invitation: 'Conversi ad Dominum' -- let us turn toward the Lord; let us convert to the Lord!"
Commenting on the trend of some to move aside the crucifix, Benedict XVI explained his feelings rather plainly.
"Moving the altar cross to the side to give an uninterrupted view of the priest is something I regard as one of the truly absurd phenomena of recent decades. Is the cross disruptive during Mass? Is the priest more important than Our Lord?"
The Liturgy of the Eucharist provides an opportunity for both priest and congregation to "turn towards the Lord," both looking with love at Jesus Christ, whose death is made present through the words of the priest.