I don't get what's so hard about the concept of "strictly necessary". If you take the cookie away and the site ceases to function such that the user cannot complete tasks they are there to do, then the cookie is strictly necessary. If the site continues to function, even if your business analytics are somewhat impaired, it's not strictly necessary and you need to gain the user's consent to set it.
Because the site may continue to function, but with reduced usability. I don't believe the new law says anything about analytics, just cookies which are not (waves hands) "strictly necessary". Just how much of a degradation in usability is acceptable is presumably a question for the lawyers.
There's a disconnect here. How does the absence of analytics mean the site continues to function with reduced usability? You could argue that over time the site's usability would not increase as much as it might be due to missing analytics data, but it won't be reduced just because the Google Analytics beacon isn't present on the page.
If you think that having analytics data is such a benefit to the user, explain to them why you want to track how they use your site and let them decide whether they're happy with that. That's all this law requires.
Again, the new law does not specifically mention "analytics" - the analytics issue is something that you yourself have come up with. If you read the guidelines, you'll notice that it states that consent does not need to be sought "where such storage or access is strictly necessary for the provision of [a service]". As I mentioned above, the provision of a service may have a usability component, for which cookies are necessary; however the service may work with degraded usability without such cookies. Would a degradation in usability make the cookies "strictly necessary", and if so, to what extent? This is something the new law does not address, and causes worry for web developers like me.
