Here’s what the Catechism says:
1457 …] Anyone who is aware of having committed a mortal sin must not receive Holy Communion, even if he experiences deep contrition, without having first received sacramental absolution, unless he has a grave reason for receiving Communion and there is no possibility of going to confession. …]
The classic example of a “grave reason” is danger of dying before you’re able to confess. If we aren’t aware of having committed any mortal sins, we are not strictly obliged to go to Confession. We can of course participate in the Mass without receiving the Eucharist.
Priests who hold Confession after Mass probably do so because they find it more convenient; but they might want to consider that penitents find it rather inconvenient.