Well, Chrome also "doesn't support" MPEG DASH: all of Chrome, Firefox, and IE11+ instead chose to support the Media Source Extensions API, which allows you to, with very little JavaScript glue, support any of these other standards you want, as well as new standards or custom streaming solutions. Apple, always the ecosystem's asshole, hardcoded HLS support into their browser and provided no way to implement any alternative as they refused to implement Media Source Extensions.
So no, Chrome should really not support HLS nor should it support MPEG DASH: Safari should just support Media Source Extensions. Apple finally did support Media Source extensions at some points on desktop Safari, which makes some sense as they effectively lost the war for the browser on macOS: no one was going to go to the ludicrous cost to support HLS (which would require you storing not just extra copies of all of your assets but also storing many copies of your audio as I am pretty sure HLS doesn't support separated streams) for Safari users given the existence and already-dominance of Chrome.
(FWIW, the cost of the duplicate storage was such a "bottom line" reason for websites to not support HLS that Apple finally decided to break a bit and support the MPEG DASH fragment files in Safari 10. It still is an extra implementation burden to support this hard coded spec and hobbles the entire industry to "whatever capabilities are sort of supported by HLS" instead of "whatever can be imagined on top of Media Source Extensions", but it no longer isn't "a major cost of our business operations is going to more than double".)
But, they still have not implemented it on iOS, because there they have control over the browser (disallowing any alternative) and are also a force in the mobile market you can't ignore (which is why this should be illegal). This means that you are forced as a content provider to support HLS so you can target iOS users (and before Apple lost, macOS Sadari), and that's the only reason anyone cares at all about HLS. HLS offers absolutely no advantages to MPEG DASH to anyone but Apple, and so would be dead if it weren't for Apple's active resistance to Media Source Extensions.
Keep in mind that while everyone always thinks that Apple does things to be an asshole or 'special' or whatever, it's far more likely that it was just coincidence or bad timing. Apply hanlon's razor and the wold is a whole lot less shitty.
Regarding HLS vs. the rest: HLS was developed around 2008 and published somewhere in 2009 IIRC, while MSE was at least 5 years later. At the same time; MSE has been supported since Safari 8 (macOS) Around 2015, according to WikiPedia, which is the same year FireFox gained support for it. Not sure about iOS.
Practically: Apple supports MSE and some DRM natively on the desktop just fine, and YouTube, Netflix etc. are using it at least since 2015 or thereabout. Also, most embedded video players in HTML5 just load a simple player framework that switches to the best available option. That might be MSE or HLS, but in the past it would also switch to Flash, RTSP and that windows media stuff.
btw, Chrome on Android supports HLS (for compatibility with lots of mobile HLS video content targeting iOS users). Pre-Chromium Edge supports HLS on Windows desktop.
So no, Chrome should really not support HLS nor should it support MPEG DASH: Safari should just support Media Source Extensions. Apple finally did support Media Source extensions at some points on desktop Safari, which makes some sense as they effectively lost the war for the browser on macOS: no one was going to go to the ludicrous cost to support HLS (which would require you storing not just extra copies of all of your assets but also storing many copies of your audio as I am pretty sure HLS doesn't support separated streams) for Safari users given the existence and already-dominance of Chrome.
(FWIW, the cost of the duplicate storage was such a "bottom line" reason for websites to not support HLS that Apple finally decided to break a bit and support the MPEG DASH fragment files in Safari 10. It still is an extra implementation burden to support this hard coded spec and hobbles the entire industry to "whatever capabilities are sort of supported by HLS" instead of "whatever can be imagined on top of Media Source Extensions", but it no longer isn't "a major cost of our business operations is going to more than double".)
But, they still have not implemented it on iOS, because there they have control over the browser (disallowing any alternative) and are also a force in the mobile market you can't ignore (which is why this should be illegal). This means that you are forced as a content provider to support HLS so you can target iOS users (and before Apple lost, macOS Sadari), and that's the only reason anyone cares at all about HLS. HLS offers absolutely no advantages to MPEG DASH to anyone but Apple, and so would be dead if it weren't for Apple's active resistance to Media Source Extensions.