My understanding is to do with water temperature at the right time of year, haven't heard about more suitable populations so feel free to enlighten me.
On our fish farm rainbows could spawn successfully In the feeder stream, the water came out of springs from chalk south downs at a constant temperature all year and escaped rainbows would find a bit of gravel and spawn ok - but this was only a couple of hundred yards of waterway! We produced the first commercial triploids in uk, the scientist (long forgotten his name) came and showed us how, from there it escalated. Think we did brownies as well later on.
I have fished for natural wild rainbows in Alaska and believe me, our version are a pale imitation of the real thing. Regards carp being introduced species, I'm fine if we get rid of them too ?.
What I've read suggests that there are some autumn spawning strains of rainbow trout but that the ones in the UK are all spring spawners. Autumn spawners would be better suited.