Its concentration in minerals is not reasonable, but extremely small.
The yearly production per human is a barely visible grain with a volume of about a quarter of a cubic millimeter. If each human would want to have a ring of rhenium, that would need all the global production accumulated during one thousand years.
All of it is heavily contended for various applications like gas turbine blades, so the price is in the same range as for platinum-group elements, which are in fact much more abundant.
If the semiconductor layers would have thicknesses in the tens of nanometer range, i.e. they would be deposited on some crystallographically compatible substrate, then such a semiconductor might be usable for expensive devices.
Nevertheless, developing a deposition method that can recycle all the non-deposited rhenium may be not easy. The deposition methods normally used frequently deposit far more substance on the equipment walls than on the semiconductor wafer. When depositing pure inert metals like gold or platinum, there are relatively easy methods to recover them, e.g. by dissolving in acid everything else. Such a complex substance containing rhenium might be obtained from a chemical reaction during the deposition, but it may be difficult to find precursors that are also easy to recycle.