As someone who frequently demands (in polite form, in comments and not always DVs) backing up one's answers with primary sources, let me clarify both why that's a good idea to prefer, and why it's a bad idea to demand the way Skeptics demands their answers' assertions to be proven.
Why is source citing deemed a good idea in general? (an answer citing a source is more likely to be upvoted[1] than one that doesn't, leaving aside downvotes)
Most people who have good questions posted here are specifically interested in things from the point of view of a source material. Any answer not based on source material may very likely be off-topic for any given specific question.
Moreover, it's very likely that a random question that is NOT interested in an answer based on source material is a bad fit for SE format; as any random speculation is an "equally valid" answer.
Please note that this is not a hard and fast rule - some genuinely great questions violate it - but it does seem to be a good first approximation.
If an answer is based on a source material, but doesn't cite, there's no way for a reader to ascertain whether the answerer made things up, or made a mistake, or was 100% accurate; except if the source material is universally well known (Vader being Luke's father can slide by without a citation... Darth Plagueus being a Muun is a lot less well known).
Some people may actually misunderstand the nuances of the source material; and answer incorrectly even with correct source material in mind (because the critical detail they are missing was in 1-2 words in the quote). Lacking said quote, people won't be able to catch the error.
Why is demanding a source material reference in every answer not a good idea?
First, because of exceptions. Some (admittedly rarer) questions aren't necessarily based on source material.
For example, this one - while not great, it's not bad IIDSSM - asked for a logical explanation of something; none of the good answers needed or had source citations except for one. Many were out of universe.
Some (again rarer) great answers aren't necessarily based on source material (see Izkata's meta answer for an example of this). They may be based on pure logic; or some "real life" fact; or general knowledge synthesis.
Additional examples: Based on real life comparison; another one based on logic and real life comparison - though the latter one also falls under #4 below.
Sometimes, you can have a good answer based in source material; but where the answerer has no easy way to access the citation (no softcopy/searcheable text; no googlable screenshots). They remember the basis of the information; but have no tangible proof of that.
Admittedly, such an answer isn't fully good until the citation is fully added; but if the answer is detailed enough, the citation merely adds finish to already good and correct content.
For example, see my (correct and based on recalling the source) answer here - and a better answer with more votes with an actual cite of the fact in the same question.
A variation of that is an answer referencing extremely well known facts from canon that are useless to cite (e.g. my answer here - one of my most highly voted - referenced well known Yoda behavior and other SW facts with zero cites).
It would be incredibly difficult to implement correctly via technology. Even Skeptics does it by hand.
There's no great need. We have reasonably decent community moderation; a vast majority of speculative answers with no cites are commented on and don't gather many upvotes (and sometimes gather DVs, though rarer).
[1] - For example, see some of the top users by rep - Thaddeus ([in]famous for posting answers with tons of comic book illustrations); Slytherincess (who was the first user on the site to obtain per-tag gold badge; and [in]famous for quoting HP books verbatim); and yours truly (also generally attempting to post quotes in good answers).