Push-to-talk—and its very disruptive nature—is apparently still a thing, because Verizon announced that it's bringing the feature to a variety of smartphones, including the Galaxy S5.
Push to Talk Plus is essentially a premium version of Big Red’s existing push-to-talk capability. It’s faster, features lower latency, has better call quality, and is encrypted. Unlike older phones that had a dedicated button for it, you access the feature through an app, which Verizon texts you the link to when you sign up. The service will add an extra $5 a month to your bill, though Verizon is offering six months for free if you sign up soon, and it's available for most of the current generation Samsung and Motorola smartphones, as well as the Casio G’zOne Commando 4G LTE, and soon, on the Kyocera Brigadier.
Of course, if paying a monthly fee for better call quality isn't up your alley, there are a ton of push-to-talk apps in the Google Play Store.