When Carplay starts up on my NEX8000, I get a warning screen with an OK button that I have to hit.  This screen invariably comes up just as I start driving, and it practically screams for me to hit OK.  It's ironic that you're acknowledging that using the radio could be a safety issue, when hitting that OK button as you start driving could be particularly dangerous.

Any chance I can get it to stop showing me this ridiculous screen every single time I start up the car?

Nope. It's mandatory, the same way going to your maps screen requires  you to hit OK. 

Be in slightly less of a hurry let your car warm up for a sec before hitting the road and press the OK button before you put the car in reverse to get out of your driveway.

My wife used to have an '04 Prius. While driving, you couldn't select the INFO button on the radio to see the name of the artist and song. Instead, Toyota provides the same info scrolling across the screen. In other words, they want you to take your eyes off the road for 5-6 seconds to read the scroll but not to see it all on one screen for a second of two.