Although I haven't been part of Math.SE long, I see a great deal of internal conflict over the issue of cheaters, i.e. people that intend to plagiarize the answers. This is separate from the issue of poor posting ettiquete (e.g. "Prove this" vs "How can I prove this"), and separate from the issue of giving sufficient details and showing work attempted so far -- all of these can be addressed by polite comments to the submitter, and none are as serious as the cheating issue.
The primary argument against cheaters is that of moral outrage; secondary arguments include wasting the solvers' time and besmirching the site's reputation. There aren't a lot of arguments in favor of cheaters, except that we don't have a good way to detect them. Responding to suspected cheaters has a wide array of approaches:
Do not answer and/or downvote the question.
Leave gaps in the solution.
Give an unhelpful solution using advanced techniques.
Downvote any answers believed to be too complete.
Close the question.
The problem with all of these approaches is that if a non-cheater is misidentified as a cheater, the submitter is not getting a proper answer, which is the whole point of this site. There is also often the implication of cheating even if the only problem was poor etiquette. Further, approaches (4) and (5) are particularly toxic, since it discourages anyone from answering anything for fear that the answer may be suppressed or downvoted for moral reasons. Some people will hide part of their answer with >! which is helpful for non-cheaters but doesn't do anything against cheaters.
Here is the alternative that I suggest. The intent is to create minimal problems for legitimate users (self-study, collaboration allowed, homework not graded, supplemental problem, etc.) but maximal problems for cheaters. Into answers for suspected cheaters, insert a copyright trap, specifically an advanced tangential technique. Should a cheater copy verbatim, the trap will immediately signify to the grader that plagiarism has occurred. However, without the copyright trap, the solution is still complete, correct, and helpful to the asker. A poster genuinely trying to understand the solution will ask about the trap, while a cheater won't.
Example Calculus Question: Find $f'(x)$, for $f(x)=3x^2+7x$.
Example Answer: Because polynomials are $C^\infty$, $f'(x)$ must exist. Using the sum rule for derivatives, $f'(x)=(3x^2)' + (7x)'$. (etc., detailed and complete answer)
Example Precalculus Question: Solve $3x-7=5$.
Example Answer: We want to eliminate the $-7$ by adding $7$ to both sides, to get $3x=5+7$. But also $5+7=12$. Because equality is transitive, we can combine these to get $3x=12$. We now divide both sides by $3$ to get
x=12/4. But also 12/4=3. Again since equality is transitive, we combine these to get x=3. $x=12/3$. But also $12/3=4$. Again since equality is transitive, we combine these to get $x=4$.
An attentive cheater might remove such a trap sometimes, but it only takes one oversight to get caught. The only way to consistently remove traps is to genuinely understand the solution from start to finish, in which case a cheater has been converted to a learner.