Should you mention previous rejections when resubmitting a paper? What is common practice?
Regarding your arguments for: 1. and 3. seem to be more like "axioms" than arguments.  1. in particular seems almost to be begging the question.  As for 3., journals have (increasingly!) long lists of requirements for authors, some of them serious but also others that those "in the know" know that they may safely ignore: e.g. many journals ask that you submit papers in their own template, but there's no good reason for that, most papers that I've written or refereed do not do that, and no one cares.  So the negation of 3. seems more reasonable to me: if journals wanted you to provide this information, they would ask for it.  (Maybe you are trying to argue that they should ask for it.  Interesting, but a different question, I think.)

Argument 2. is much more pertinent: if the referee's careful opinion is that your paper is valuable and deserves to be published in a research journal but just not in the journal that you have submitted to, one can indeed save a lot of people's time by carrying over the same referee to a different journal.  If you want to do this, it seems best to ask the editor of journal A to get in touch with journal B.  I've done this both as an author and as the carry-over referee.  

But this is an option that the author gets to choose to exercise or not.  In terms of the current practices, this is certainly true and I don't think anyone expects otherwise.  Again, it is interesting to argue about whether it should be true....and yes, I think it should.  The refereeing system is not strong on incorporating "responses to referees": when authors write back to the editors pointing out factual mistakes in a referee report, they are often told something like "I am inclined to believe you and that is most regrettable.  You should definitely resubmit your paper to another journal of similar stature.  Best of luck."  Very often the referee acts not only as the jury but also the judge and the executioner in the current system.  But for a paper whose work is agreed to be correct and novel -- or for which this evaluation was not even made -- then fundamentally, "not good enough for a journal like X" is nothing but an informed opinion.  If that opinion is a sound one, a different referee will probably come to it independently.  If it isn't, then I think the author has every right to start out fresh.

Let me also say that as a frequent referee, I do not feel the desire to know the provenance of the paper, and I don't think that would help me with my decision.  I already have what I think is probably too much information at my disposal: namely the author's identity and thus their professional reputation, my personal view of them, and so forth.  Being a good referee doesn't mean taking all possible information into account; it means taking exactly the right information into account to evaluate the paper on its own merits.

In the course of arguing against the "arguments for", it seems that I have espoused some of the arguments against: 2. and 3.  I hope these arguments have been shown to be more convincing.  (Arguments against 1. and 4. do not seem very compelling to me.)