An undiagnosed or unreported mental health issue isn't a "crack in the system".
The problem is, that's counting on the general public to listen to what they don't necessarily want to hear. It's counting on the general public to use critical thinking.
People seem not to be wired that way. They want 30-second soundbites they can easily digest. They listen to whichever Twitterina can make the most "sense" to them in 140 characters or less.
The general public listens to emotional appeals and does a terrible job of checking sources. In that situation, if my 30-second soundbite is less compelling than the opposition's, guess who wins?
That's why we have to be very careful about what we say, and how we frame it.
If a sense of caution discourages an appeal to prudence and reason, then it isn't truly caution. A feckless anxiety that people who already oppose a right will belittle an argument can look more like a dithering countenance and lack of confidence than sober caution.
While the analytical capacity of lots of people seems like a sound basis for a bottomless anxiety about the future, the "general public" aren't a homogenous mass. Lots of progress can be made at the margins where people observe and are persuaded. In the wake of each one of these tragedies, a sort of reasoned argument is made by restriction advocates: a gun caused a harm, so a restriction on guns will restrict the harm. We are too familiar with the problems present in that reasoning, but it is a [poor] reasoning.
Broadly, three sorts of response are immediately available.
1. No response at all. This looks like an admission -- a reasonable person confronted by the opportunism of post tragedy calls for suspension or restriction of rights will voice his disagreement. If you are Jeb Bush and you are asked whether you support re-imposition of the AWB, no response is both a personal defeat and a concession on the issue.
2. Call for an intermediate restriction to relieve the political pressure for greater restriction. This may be some of the motivating force behind calls for more strict mental health controls.
3. An explanation as to why further controls are not warranted.
Is the aftermath of high profile murder the time for this sort of argument? Yes. It is the public focus on the issue that draws draws the opportunistic calls for restriction. Responding later when the issue has passed public notice isn't effective. For people not interested particularly in this area, the attention span is likely quite short and if your position isn't out quickly, it largely isn't out at all.
So, a "good guy with a gun" may be mocked by some. Chris Mintz took seven bullets trying to stop the Oregon killer while his firearm sat in his car. Isn't the Oregon incident an example of a "good guy without a gun"?
That succinct explanations of the problems with politically expedient non-remedies meet public opposition from opponents of the underlying right isn't evidence that they are poorly timed or tone deaf. The argument is going to happen after these events; neither you nor I have a choice in that.