I have a rear top rack back and I keep my phone in there. I have a ziploc bag in it in case it rains etc. If you're looking for the racer aesthetic I suppose that wouldn't work. For mountain biking I got a hard sided case that goes in my rear underseat bag.

I have no idea why anyone would say with a straight face that going riding without a cell phone is a good idea. A cell phone is a magic device that lets you communicate wireless with anyone you want including uber/lyft/taxis or emergency services. Why would you ride without it? Just be an adult (or actually perhaps a teenagers as they never answer their phones lol) and don't use answer your phone if it rings. Not hard. I see no reason to deal with the possible hassle of getting stranded or the rare emergency life threatening situation and not be able to get ahold of someone because you didn't bring your phone with you.

Cell phones have also made group rides a lot more mentally enjoyable for me as I know if I get dropped, I can always get back to my car via google maps or uber. One time I biked to the gym, locked up my bike, when I came out I tried to unlock my bike - something has failed inside the lock and it wouldn't unlock. As I had my cell phone with me I didn't have to go through a long tedious walk back to my car, or deal with the hassle of calling a friend and bothering them to pick me up, I just got Uber and for $10 got a ride back to my car. When I came back to pick up my friends bike my lock had started working again and I was able to unlock it so altogether it was basically no big deal.