Just about every music player app has a random mode, so you still just fire it up... seems like marketing has made you forget this has been true even before most people had cell phones, even the portable MP3 players of 15+ years ago could do this, just didn't have enough memory capacity for several thousand songs at the time like a mSD card (or more expensive phone with more built-in memory) can today.
Further, unless it has changed recently, pandora is only 64Kb rate for mobile and no higher than 192Kb otherwise, a low bitrate for audio that IMO ruins treble. You can fit roughly 20,000, 256Kb MP3 songs on a $13, 128GB mSD card today. As it pertains to driving, you don't even need to use a phone, can pop that 128GB mSD card into a sub $15 standalone, cigarette lighter outlet powered player. If you're a "very busy professional" who needs to use the phone a lot for other things, it seems like a great idea to save phone battery life... tho' I don't think it has much to do with being busy or a pro, just whatever use habit you get into.