If Joseph asked Pilatus to retrieve Jesus' corpse it means he must have had access to Roman elite in Palestine. Would not have Joseph been seen by Pilatus as another potential trouble maker? Would not have Joseph been reprimanded by the Sanhedrin itself with such an action?
Josephus of Arimathea is described in Mark as a 'respected member of the council', i.e. he already is a member of the Jewish elite, and that would explain why he could access the Roman elite. It's quite consistent that a leading Jewish figure could make an approach to the Roman governor.
while there is evidence that Romans refused to bury those crucified, there is some counter evidence that at least in Jerusalem it was typical to bury victims in accordance with concerns abut purity an Jewish law. This includes Josephus Jewish War 4.317, which refers to rebels in 66 CE not burying the dead, in contrast to a more typical pattern of even burying crucifixion victims. This suggests that even the Sanhedrin was unlikely to oppose Jesus' body being removed and buried.
The account as it stands is plausible.
I'm no historian but I know we don't take the gospels as true stories; do historians have any reason to believe Joseph of Arimathea actually even existed? I mean this question supposes that Jesus did, and during the reign of Pilate, and that he was killed in a manner at least similar to what the gospels describe, but I think it's pretty safe to say we don't have any reason to believe that's true, yes?