Relatively speaking, removing the corpse's clothes would cost significant time and effort.1 This is relevant because people don't waste time and effort unless they have good reason, especially if they are thieves.2
Merrill Tenney (NT Professor at Gordon College (d. 1985)]): “In preparing a body for burial according to Jewish custom, it was usually… bandaged tightly from the armpits to the ankles in strips of linen a foot wide. Aromatic spices, often of a gummy consistency, were placed between the wrappings or folds. They served… as a cement to glue the cloth wrappings into a solid covering…” [The Reality of the Resurrection (Moody, 1963), 117.]
John Chrysostom (Early Church father): “Especially when it was myrrh, a drug that adheres so to the body, and cleaves to the clothes, whence it was not easy to take the clothes off the body…” [Homily 90 on Matthew 28; 11-14.] “…glues linen to the body, not less firmly than lead.” [Homily 85 on St John]
The stench of the putrefying corpse would be exacerbated if the clothes were removed. This is relevant because any body-movers would clearly not prefer this.
If the graveclothes of Jesus were removed, then likely the removal process, rebandaging process (if that was involved), and moving of the corpse would involve touching the corpse's body directly. This is relevant because as much as people today are disinclined to touch a rotting corpse (out of revulsion and/or superstition), ancients were even more disinclined.
Removing the corpse's clothes would be considered egregiously shameful to the corpse. This is relevant because while perhaps some body-movers would be less fazed by it, like all, they would consider it a demotivating factor. In a superstitious honor-shame society, which the residents of Jerusalem were in, actions like this are taken especially seriously.