Because the iPlayer is not Sky Go. Sky Go has more complex DRM requirements due to the multiple sources the content comes from (different film/tv studios, different sport franchises etc.).
Currently, Silverlight is the DRM system/software used by Sky Go; this will have been chosen (and agreed on) to meet the protection requirements of ALL the content providers. Since Silverlight no longer works with Chrome, Sky Go no longer works with Chrome.
To replace Silverlight will not be a five-minute code change. They will need to find a suitable DRM method to meet at least the same protection standards as Silverlight, then most likely change the entire back-end setup to use the new system, before re-writing all the various websites and apps (iOS & Android, Sky Go, Sky Sports AND Sky Movies apps) to use the new back-end setup.
It is entirely possible this changeover is already ongoing behind the scenes. Ultimately Sky don't announce changes like this as it is, to a great extent, invisible and irrelevant to the end user.
The first we as users are likely to know about it is when they release new versions of the apps and/or suddenly announce support for Chrome again, or even support for Edge.
Ultimately, it is what it is, and there is nothing we as customers can do about it.