It's adds to your credibility and reduces how threatening you appear when you snap a photo of someone in public. If you're using your phone, the subject's assumption will be that they are about to be plastered all over your social media. If you use a huge DSLR, you come across as creepy.
If you're using something odd, unusual, uncommon, like a film rangefinder camera or digicam, it's much more clear that your intentions are not evil, and that you simply really like photography. I've had curious people ask me about my camera after they notice me take a shot of them, which would never happen if I had used my phone.