Before I say anything else, it is important to realise that international politics is, in general, a game of presenting one's own worldview and stated objective in the most favourable light. Acknowledging any other side's views is, as a politician in international relations, a tacit admission that there is a certain truth within them and there is a reasonable assumption that a common ground can be found including those views. Conversely, if presented in the appropriate diplomatic ways and contexts, it is easy for any party of international politics to ignore what the other side has said after stating their own view of the issue.
As an example, consider a press briefing after a discussion between two heads of state or government where one side states 'I reminded my colleague about the importance of guaranteeing the rights and representations of [national minority]' and the other side says in their opening statement 'I reminded my colleague that our recent general election was free and fair according to our laws and that the considerations of all parts of the country were addressed.' The facts about the rights of the national minority or the free and fair election might be anywhere; both sides have stated what they believe and they can move on to other issues where they might actually have a chance to find common ground.
This brings me back to the question as you asked it and I am going to answer it not in the order 'Western media, Western discussion, and even Western politicians' but in the order that is best for the explanations.
For western politicians, the case is clear. They are political actors in international politics. Everything they say or do is intended to give their spin on the issue. If they disagree with what the other side says, they can either outright dismiss the arguments (which is akin to saying they consider them wrong) or ignore them (which is akin to saying they might be correct but I don't want to talk about them). Of course, their goals will mostly be their own national interest – in some cases also the interest of multinational organisations such as EU, NATO, Council of Europe, OAS, etc. – and therefore what they say and which arguments of the other side they accept or consider will always align with their interest. (It is worth noting that sometimes the national interest of different politicians differs. For example in Germany, the party AfD has a very different view of national interest than all other parties represented in parliament but especially than the current centre-left government.)
Western media and media all over the world in general has two goals although the relative weight given to the different goals varies depending on media outlet, ownership thereof, national laws governing the media and editorial position of the media outlet. These two goals are: (1) identify and report the truth about events; and (2) further the narrative that whoever is in charge wishes to push.
Ideally, we would wish for all media to put most weight on goal number (1) but that has never been the only goal and it is not feasible as an only goal. Reporting facts has always and will always be accompanied by commenting on facts – and I very much include this answer and the whole of Politics Stack Exchange in that observation. Nevertheless, there are many media outlets which attempt to put (1) to the front as much as possible, many in which (1) and (2) are balanced in a way not always obvious to the public and many in which the primary objective is actually (2) (I see this site in the first bracket).
When it comes to reporting on states' objective as per the question, these two goals will lead to two different reporting styles.
Where the underlying facts can be verified and determined to be true or false, media outlets will report as such depending on their relative commitment to goal number (1). However, where the facts as per goal (1) directly oppose the editorial position as per (2), well, it gets complicated.
Where the stated objective is not so much fact-based as opposed to opinion-based or a motivation to achieve a certain future outcome, reporting style (1) cannot really kick in except for the few foundations that can clearly be determined to be factual or not so. Instead, a large part of the reporting will be of the second style, i.e. more influenced by commentary and editorialisation – at least after the goal has been repeated.
Media outlets' editorial positions – i.e. consideration (2) – is where the answer to your question is essentially buried. For the most part, states' stated objectives are not so much fact-based but rather a desire for a future outcome. In part, this is because of how easily some facts can be proven true or opposing statements proven false.
There is a general observation that the editorial positions of many media outlets seem to reflect what politicians consider national interest to varying degrees. In some cases, this is not surprising because the predominant media outlets are owned or controlled by either flat out the government itself, individual politicians or wealthy individuals whose interests align with the government in power and these decide to exercise editorial control. The more this is a top-down process and the more hands-on the government exercises control, the less free the press is said to be. In western countries, some media outlets receive a large percentage of their funding from the government (e.g. British BBC, German ARD/ZDF/DW, Finnish YLE, Japanese NHK); however, it is important to realise that the approach is far more hands-off and that funding typically cannot be increased or decreased in the short term following favourable or unfavourable reporting. Therefore, one cannot simply equate funding by the government with less free press.
That said, however, even in free press countries the interests of media outlets and politicians might overlap to a frightening degree. This can be explained by looking at the countries as a whole: it is the same population that elects politicians into power and buys/consumes media for their circulation. Therefore, a significant overlap between what the public thinks, what politicians say and what the media writes is to be expected even in a fully free society, even where we are only considering the editorial positions. This paragraph does simplify, as both politicians and media outlets can (and do) push agendas on the public, influecing the public's opinion and reinforcing the pushers' goals. For an impressive historical example, look at how the Nazi Party and right-wing to far-right publications influenced public opinion in late 1920's and early 1930's Germany.
This brings us to the third part you asked about, public discussion. Obviously, public discussion cannot be separated from the interests of politicians and the media – indeed, those two groups form a significant part of public discussion. Therefore alone, it is already far more likely for public discussion to align with politics and media if the latter agree than it is for public discussion to disagree. Note that exceptions do exist: occasionally voices in public discussion that are not part of national parliament or government, and are not well-represented in the majority of media editorial positions, but which do represent a majority of public opinion, are able to sway politics and media in their direction.
All of this combined will show that, indeed, using a 'both sides' approach is the exception because it counteracts one's own side. The other side's views and objectives are typically only picked up and amplified by opposition politicians if they think the government is in the wrong or news media if the government is acting counter to the outlet's editorial position. For varying reasons, politicians, media outlets and public discussion has a tendency to gravitate towards a common view, especially when the conflict is perceived as 'us versus them' in the broadest possible interpretations of us and them. This, of course, will lead to the other side's view being neglected, ignored, disproven where factually possible or disregarded.
(Going through each of your example conflicts and highlighting why in that specific case such a general consensus (seems to) exist requires looking at them individually, doesn't really fit the scope of the question as asked and would increase the size of this already huge answer exponentially.)