However, look at the flip side of it:
Sky use Silverlight because that is what they agreed with the content providers would be the DRM system for Sky Go, so it is more than likely a condition/part of the licensing contract.
Sky use Microsoft's recommended method of device ID generation.
Microsoft then decide to change how their OS updates are applied and as a result manage to break their own product each time.
For Sky to make any change to Silverlight or the way it works is likely not a simple task with the hoops to jump through to meet the contract obligations.
Given that, as everyone keeps pointing out, Silverlight support in all major browsers will be virtually gone within the next 12 months or so, I would imagine they are more concerned with planning/developing a replacement for Silverlight than fixing what is (or really should be) a relatively minor inconvenience if handled correctly at customer service level.
Is the problem with Silverlight Sky's fault? No.
Can Sky fix the problem? Possibly, but likely a major undertaking which would be a waste of time and resources given the current ecosystem.
Can they handle this better from a customer service/PR persepctive? Absolutely.