But they use much more power when they are receiving data.

Sending data with a radio is always much more power intensive than receiving data unless the channel is extremely asymmetric in bandwidth and/or data rate.

Sure. But they also use a massive amount of power when they’re out of range so constantly searching for the network

Turning off your modem is second only to turning off your screen if you’re looking to save battery

Not nearly close enough to when they are receiving data, especially video.

When actively receiving data, a cellular modem will use significantly more power than when idle, with the exact amount depending on factors like network strength, data rate, and the specific modem technology, but typically ranging from several hundred milliwatts to a few watts