I don't think it's too onerous. I've seen pretty ordinary looking cable in printers before, either ~1oz and probably around those substrate thicknesses, or the embedded-flat-wire kind (the stuff that's rather substantial feeling, seems like the copper is thicker than the carrier; don't know if you can get PCB made that way, but they're commonly available as plain cables at least).
Some supporting material may help enforce the bending radius constraint. For example, thicker but also more flexible tape, or foam, glued to the cable (one or both sides). Don't forget strain relief, so the cable, with any stiffeners/springiness-ifiers, are anchored to mounts, keeping flex away from the connectors.
What kind of cycle life are you expecting?
I think you could calculate cycle life, based on the moduli of copper and polyimide (or whatever substrate), layer thicknesses, and the fatigue limit or curve of copper.
The copper foil won't be dead-soft, but; well, hm. Raw foil might be annealed, but is more likely supplied half-hard or thereabouts? Plated copper, isn't actually dead-soft (as you might think from the purity?), but contains internal stress due to plating and additives, and, is probably somewhere in the half to full hard range in terms of hardness, but is weaker than a rolled product of the same hardness.
Hah, wow, never thought of that before but it's amusing -- if the stackup is all polyimide and other high temperature resins, I bet the copper could actually be effectively annealed by heating, without compromising the substrate strength too much. Polyimide is rated to crazy temperatures, right around where copper starts to anneal I think.
Anyway, a bit rambly, but should be good for insight and leads on what to look for. Cheers,
Tim