I really wouldn't say that 4k is better in every way, both technologies have their advantages and disadvantages:
First, 21:9 monitors can also be higher resolution than "extended 1080p", when compared with similarly priced 4k monitors, they normally have the resolution 3440x1440. This resolution requires far less horsepower to game on than 4k, but far more than a 1080p or even 1440p display. It is also very helpful productivity, replacing multiple monitors. Though the resolutions(meaning all 21:9 resolutions) are not supported in some games, in most of them it is supported and reportedly delivers a very immersive experience (as stated by Linus himself). Some people also just plain prefer multiple monitors or just one normal 16:9 monitor.
4k "just works", like 1080p, but just improves the resolution compared to a 1080p monitor. While that's great for a lot of use cases(including gaming, if you have the horsepower!), it does not necessarily give a productivity boost, since UI elements have to be scaled up, meaning that the gained pixels do not necessarily increase the workspace (all other things being equal).
Both 4k and 3440x1440 (21:9) do not support very high refresh rates and need a lot of horsepower, so you could just look at a 1080p monitor, maybe even with 144 Hz / good color and contrast / GSync or Freesync.