I myself own a cassette tape player, because there are a few music clips inaccessible to the public forms of streaming media.
I wouldn't say there's something magical about using a Walkman, but there is something practical about just pressing a single button and having the music play without delay.
I would say it's practicality and pragmatism that's missing from most stuff deemed retro.
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I definitely agree---it's odd because the Internet arguably is more easy to use today than ever (accessibility features aside, the standard web 2.0 look is *functionally* simple). But like you mention with the Walkman, there's nothing special inherent to the device, but there's a purpose. I think many use the Internet nowadays not only on our laptops or computers, but our phones, watches, smart devices, etc. that we lost that pragmatism you mention that was prevalent with the early Internet. It's not just a place to browse, shop, and message friends after work. It's now imbedded in our lives in a way we can't permanently untangle ourselves from unless we go cold-turkey.