Is "can't" a statement they should be expected to support/prove, or can it be placed down as an unsupported matter of opinion?
All answers are expected to be supported regardless of whether they're a "don't/can't" or not.
How much due diligence does an answerer owe the community, before tossing down "can't"?
The same amount of due diligence required of any answer.
There's a difference between saying that something "can't" be done and saying that something "shouldn't" be done. Obviously this being a site about interpersonal skills, a great many things technically can be done that perhaps shouldn't be done. For instance, if a question asked:
How do I hit on my best friend's wife?
Two answers immediately present themselves:
Don't hit on your best friend's wife, because... (reasons)
If you're going to do it, ask if they're ok with it first, or don't get caught doing it because... (reasons)
Now obviously you can in fact hit on your best, monogamous, friend's wife. But is this a "good" answer? Here problems arise because people have different opinions about what's "good."
Most likely the majority of people will support the "Don't do it" answer, but there will probably be at least a few who will lean towards the "Don't get caught" answer. And, well, believe it, or not, these are both answers to the question asked. One told the OP not to do the thing they wanted to do, and the other gave possibly ill advised advice on how to do it.
Now, if the question had been:
How do I hit on my best friend's wife, without running the risk of offending him?
The only reasonable answer is probably going to be:
You can't hit on your best friend's wife without running the risk of causing offense, because... (reasons)
Regardless of the question, each individual answer isn't expected to be exhaustive. It's great when they are, but it's an unreasonable expectation. Each answer is only required to be one self contained answer to the question. And, like it or not, frame challenges are permitted.