Bitstream is both chip- and board-dependent.

Chip-dependent quite obviously because FPGA is a complex two-dimensional (or even 3D) device, not an array of bytes, or 72-bit words, etc. according to some JEDEC standard.

Board-dependent for the same reason: which signals go to which pin of the chip isn't standardized either. Some dependencies could be resolved, but it isn't clear that the boards are compatible enough. It was discussed at the beginning of this thread.

Additionally some boards may not have enough power to continuously supply the required current for full performance. You would then be forced to severely under-clock them to avoid tripping the on-board over-current protection.