Well, the Roman Rite really drives the Passion down our throats during Holy Week - but to a lesser extent now compared to then. In the pre-1970 Lectionary, the Gospel readings from Sunday to Friday, excluding Holy Monday and Holy Thursday, are the Passion narratives from all four Gospels:
Palm Sunday: Matthew 21:1-9; 26:1-75; 27:1-66
Holy Tuesday: Mark 14:1-72; 15:1-46
Holy Wednesday: Luke 22:1-71; 23:1-53
Good Friday: John 18:1-40; 19:1-42
What is interesting is that originally around the time of Pope Leo the Great (400-461), Matthew’s Passion Narrative was used on Palm Sunday and the following Wednesday and John’s on Good Friday. Eventually, Luke’s Passion became the Wednesday Gospel while Mark was chosen for Tuesday somewhere around the 10th century, giving us the above order.
It was all due to the fact that originally for the church of Rome, the Sunday before Easter was just Passion Sunday. When the Roman Rite became hybridized with the Gallican family of rites around the Carolingian period, the two customs merged and Sunday became Palm Sunday, while the original name was applied to the Sunday before Palm Sunday.
Before 1955, the Blessing of the Palms was a more larger, fuller service. Now, back then and even today, the gospel read during the blessing is indeed the triumphal entry. So it’s not like we don’t read them.
Personally, I think the Passion serving as the main Gospel during this Sunday in the Roman Rite is intended to be ironic and juxtapositional on many levels: the crowds greet Jesus as a triumphant king, but Jesus’ kingdom is not of this world. Many of the people who greet Him with Hosanna would also be the ones who will shout for His execution days later.