I can't offer a full answer but perhaps part of a relevant answer.
▻ PHILOSOPHICAL SYSTEMS
Even if analytical philosophy is averse from system-building, it is impossible to do analytical philosophy of any kind with a background of assumptions and presuppositions, and without one's work having a range of implications. The totality may not be a system but it is system-like.
System-building remains a possibility and does still go on. YW's question is therefore proper and pertinent.
▻ PHILOSOPHY AS RHETORIC
I found this quote useful :
Philosophers make claims about the nature of things, the nature of knowledge,
the nature of human existence, and so forth. These claims must be tested by
argument. In argument, philosopher aim at validity. The principles of validity
are determined in logic. Philosophy is about controversy; it is a critical
activity. When there is disagreement in philosophy, formally valid arguments
can be produced by both sides. How are philosophical disputes to be resolved?
In disputes occurring in fields of empirical and scientific knowledge there
are open avenues for their resolution. Such fields contain methods of
experimentation and investigation that allow for the production of evidence and
facts that can settle such disputes. But, in philosophical reasoning, what can
count as evidence or as a fact is itself in dispute. A fact is a fact only in
accord with a specific theory. In philosophical controversy it is the theory
that is in dispute. (D.P. Verene, 'Philosophical Rhetoric', Philosophy &
Rhetoric, Vol. 40, No. 1 (2007), 28.
The upshot is that, faut de mieux, much philosophy is a form of persuasion, with arguments, examples, topical references, appeals to emotion, invocation of parallels, all wrapped up in an attempt to bring the reader or listener around to a point of view or to loosen the hold on them of a different point of view. This is rhetorical in the same way that an attempt to persuade us that a particular interpretation of 'King Lear' or James Joyce's 'Ulysses' is the correct, or a powerfully illuminating, one. There can be no demonstration or proof, but nor need there be any reliance on fallacy, sloppy expression, deliberate irrelevance, unclear thought, falsity, or any of use of the darker side of rhetoric.
▻ PHILOSOPHICAL SYSTEM AND THE APPEARANCE OF INTELLECTUAL ARBITRARINESS
Take the examples of Hegel and Heidegger. These are on any account 'difficult' philosophers. There are sentences in Hegel which, try as I might, I cannot understand. The same experience occurs when I read Heidegger. The work of these thinkers can seem a stream of incoherence with sentences that are unintelligible or when intelligible, disconnected. Seem. Yet if one persists, both these philosophers can be seen to have views which broadly cohere within their own frameworks and often penetrate far beyond what one imagined at first look.
There is readily an appearance of their 'saying what they like' but that appearance fades as one goes deeper into their work.
▻ PHILOSOPHY AND ARGUMENTATIVE RIGOUR
But philosophy is not all rhetoric and the appearance of intellectual arbitrariness. A lot turns, I think, on whether philosophy is done in a free-standing way or continuously with other activities and inquiries. By 'in a free-standing way' I mean without tight connection to any other discipline - maths, physics, history, art or whatever.
For instance, Quine is famous (or notorious) for his view of philosophy as continuous with science. Working outwards from science, or rather maths in his case, he was constrained to work from mathematical problems and assumptions to a logical theory that was plausibly adequate to them, and to an epistemology that not only 'nested' maths in the right place among the sciences but also related the sciences to other disciplines. What's more, and vital, is that he was not the judge of his own success. He may have been a robustly independent thinker but he had to produce ideas and arguments that fellow mathematicians and scientists could accept or find useful to argue against. And an epistemology, finally embodied in his idea of the 'web of belief', in which historians, geographers, 'ordinary believers' and others, could recognise their place. This couldn't be done by simply saying whatever he wanted to.
In other fields, too, there are constraints if one starts off from a particular field of inquiry. The Italian philosopher, Benedetto Croce, began his intellectual career as a historian. As he reflected on his activities as a historian, questions pressed themselves on him about the nature of historical study. In answering these questions he had to work out responses that, whether they accepted them or not, and were interested in them or not, other historians could understand as coherent and relevant to their discipline.