Nowadays, when it would take less time to Google the difference between "its" and "it's" than it would to look up in even a slim, 100-page style guide?
Whenever you don't have wifi on your laptop. For many, that means roughly any tie they aren't specifically at work or at home.
Elements of Style is a relic of the past.
By the very same argument, so is CMoS, because anything in there can be looked up online as well. The issue isn't actually about the form factor, but about the scope - a source with a large scope is very difficult to search, especially if you don't know the exact name for what you are looking for. The limited scope of Elements of Style
makes it very easy to use for the most general of writing tasks.
Of course, this critique also assumes that you trust the internet to answer your questions, which is... perhaps not the wisest assumption to make. I suggest that the value in these things comes from their accepted authority, which "the internet" doesn't have.
Worse still, Elements of Style treats many rules as dogmatic when they are, as many things are in English grammar, quite flexible; and that's at best.
The same can be said for CMoS. Any time you have an authoritative source, this will happen - check it out, we all have PHBs, and we then argue over what rules changes are appropriate!
The point of a style guide is to be prescriptive! The highest value in CMoS to the academic world, for example, is in its prescriptive definition for references. The point is to have everyone using the same format, so that everyone can read the condensed form of information without ambiguity. If you give information that isn't in the agreed-upon format, you can print it, but the audience won't know what it means, and will not be able to find the referenced information!
My writing teachers were all pretty clear on this point - first, know and follow the rules. Only once you know and follow the rules can you choose to break them specifically to generate the impact you desire. For this to happen, the rules must be agreed upon first, and that's what style guides (and, indeed, grammar and usage rules in general) are for.