When this happens to me I know it's operating 100% on battery because the mpg from start stays at 99.9 and I can see the battery draining regardless of how quickly I accelerate or speed. The battery nearly drains completely before the motor starts. I'll post an update if I learn anything from the dealer.
Yes this is normal Hybrid Synergy Drive operation. I've owned 3 Prii and none have acted like that. All that constant cycling of the battery is going to be hard on it over time I'm sure. And in reality it probably hurts fuel economy too! You might have gotten a lemon, and I know that you don't want to hear that but I haven't heard of this happening before. I would love to drive your car and see what's up, but I'm in Nashville, so that's a little far. Keep us posted
I think I know why the ECU is acting like I mentioned. When that scenario occurs, the temperature of the gas engine is kind of in between: it's not that cold, however, it's not completely warm. Hence when the speed reaches 45mph, the ECU decides to take the safe side, to draw power more from battery.