In the United States (and possibly other countries), what are the reasons behind Jewish funerals always having closed caskets?
Out of respect for the deceased, we do not put bodies on display. Even the mourners (the immediate family) only look long enough to confirm identity. As Dr. Ron Wolfson writes at My Jewish Learning: "The deceased is a [nireh v'ayno roeh], someone who is seen but who cannot see. To open the casket and allow people to look at the deceased is to turn the comforters into spectators and the deceased into an 'it'."
From the moment of death the body is treated with respect. There is a process of taharah, cleaning and dressing the body for burial, usually performed by a community's chevra kadisha, who are specially trained in this. The body is also watched by a shomer at all times.
Judaism 101 provides an accessible overview of burial and mourning practices. That site says that not displaying the body is halacha (not just custom) but does not cite a source. You might also find this essay (Chabad) enlightening.
See the pertinent text proof from the talmud Gemara in Moed Katan 27a
בראשונה היו מגלין פני עשירים ומכסין פני עניים מפני שהיו מושחרין פניהן מפני בצורת והיו עניים מתביישין התקינו שיהו מכסין פני הכל מפני כבודן של עניים
Rough Translation: Originally they would leave the faces of those who were wealthy uncovered [at the time of the funeral], and they would cover the faces of the poor which were dirty, due to their hunger, and so the poor were embarrassed [due to this contrast], thus the Rabbis instituted that all faces [of the deceased] should be covered, for the sake of the dignity of the poor.