These days, a lot of people use iPhones and Android phones as digital music players – on top of everything else. If you have an iPhone, you can load music purchased on CD onto it, in much the same way that you would load it onto an iPod.
Sync your iPhone, iPad, or iPod using your computer - Apple Support
If you are worried about a player getting damaged or stolen, there are third-party digital music players that you can buy. I'm guessing that by now, most will play both MP3s and non-DRMed AACs (including iTunes Store purchases). But the procedures to load one will be different than for the now-discontinued iPods and iPod touches.