Judging by all of the comments complaining about DRM and having to buy new audio equipment, it seems like few people are actually reading the whole article. USB-C can support analog audio output via audio adapter accessory mode[1].
In the near future you'll be able to buy passive USB-C→3.5mm cables for cheaper than normal USB-C→USB-C cables. You will be able to use them like any other aux cable.
Personally, I still prefer the 3.5mm jack so that I don't need a passive adapter for using my earbuds. Requiring a passive adapter that gives you a perpendicular 3.5mm jack, no matter how small, would be ugly and obtrusive.
Fortunately, at least for over-the-ear headphones with a 3.5mm jack, this will at least be much less of a hassle. Passive USB-C→3.5mm cables can just be your new aux cable.