The Catholic Church does have iconoclasts within it. I was talking with my grandmother once who is a devout Catholic how after Vatican II, many of the very beautiful Catholic Churches in the city were gutted and many things were gotten rid of. She said that some parishes ripped out many of the beautiful statues and pretty much junked them (either they were thrown away or they are collecting a large amount of dust in a forgotten corner of the church basement) and other traditional things were taken out. Plus the music used in the majority of the Catholic churches here is horrid, many of them using Protestant hymns and instruments other than the organ (meaning guitar and drums). With these disregards to tradition, I wouldn't be surprised if many relics were thrown in the garbage. I do believe though that there is one church here in my city that is part of the society of Society of St. Pius X who have been able to preserve traditional Catholic piety.
I'm not Roman Catholic (used to be) but I do think it is terrible of how modern a lot of Catholic Churches are now a days. I do hope that they will one day be able to return to their older traditions.