I think the problem with communicating a logical chain of thought is that it presupposes the idea that logic is immutable and continuous throughout the chain. In sciences, logic is usually fairly immutable because it's not the object of study, so you can show the ideas, without context, and they'll make sense because the frame of reference is constant.
In philosophy, it's usually the case that if you simply presented the idea, without reference to the thinker, you'd definitely provoke misunderstandings, if not incomprehension. Philosophers don't have a common conceptual vocabulary, so when you think a given thinker is referring to a given idea (say, logic) you can really only say for certain that they're referring to their understanding of the idea.
Further, they don't have a common vocabulary for describing ideas - often to the point that you get 'young' and 'old' versions of the same thinker (for instance, Hume) because they use words in different ways within their own corpus.
So, if you wanted to present a logical chain of ideas, you'd have to develop first, your own logic that is a superset of all the contained systems of thought. Then, you'd have to develop a vocabulary that unifies disparate concepts without reducing their complexity.
Predictably, most philosophers have come to the conclusion it's easier just to organize thought by thinkers rather than ideas. Non-philosophers tend to see this as some kind of veiled appeal to authority - but it isn't really. Philosophers are very happy to pervert, break, or alter the corpus of a given thinker in order to do something new with it.
The strength of philosophy depends on rigorous questioning, and rigorous questioning does not tend to lead to monolithic bodies of thought - and that's what you'd need to produce the kind of logical and lexical superset an idea-oriented approach would need to be practical. Without substantial agreement on very many basic questions, such an approach would undoubtedly just do violence to the ideas.