Why are measurements of the magnetic field inside a rectangular coil not taken very close to the wires?

Self-answering.

Most instruments for measure are made of metal, pherous or not, and would thereby be subject to the magnetic pull at present (as would any digital devices).

Additionally, the rectangular nature of the coil would mean that there would be a concentration of magnetic force in the corners, whereas a circular coil would be evely distributed.

Also, any contact made with the wires would effectually "drain" the magnetism from the wires/coil and redirect it wherever the measuring device ordained (perhaps to your hand, though you may not even feel it; depending on how strong the magnet was). This is not to say that the magnet(s) would cease to be magnetic, but rather the(ir) pulling force would have a place to go, so to speak. Think static cling.