Yes, the tactile element and the thrill of tuning in distant stations is what has kept me in this hobby since the late 1950s. It's also nice to get away from the computer once in a while, which is one of the reasons I've never considered buying an SDR.
Besides those tunable receiver sites online, there are some internet streams from international broadcasters that have left the airwaves and switched to the web. Radio Romania International is both on the air and on the web, streaming its broadcasts in real time, including its interval signal. Some stations that are both on the air and online merely offer streams from prerecorded scheduled programs, or downloadable files of them. Radio Havana Cuba is one example. Frankly, after having used the internet for 26 years and computers for 42 years, I'm getting bored with both.