I have no problem with this. Nearly all the mass shooting are done by crazed individuals not responsible gun owners.
The problem is more complicated than that. First, you can't deprive someone of a constitutional right without due process. The SSA working with the FBI and the psychiatric community without judicial review is not due process.
Second, there are a lot of different mental illnesses, most of which do not create "crazed killers." Someone with a mild neurosis or a debilitating fear of spiders is mentally ill. An umbrella denial based on a generic diagnosis of mental illness would put the burden of proof on the citizen to show why he/she should be considered a safe gun owner. That's wrong. The burden should always be on the government, by due process, to show the gun owner has forfeited their constitutional right. That's a much tougher case to make, but it's the right way to go.
Third, there is no reliable connection between being a poor manager of one's financial affairs and having a mental illness that makes one a genuine danger to themselves or others. So even if we just accepted the violation of the constitutional principles, we still have a "test" that is too broad to be effective in accomplishing it's stated purpose.
Fourth, overbroad laws are typically very easy to shoot down (pardon the metaphor) as invalid. But they are very good tools for social engineers who have no desire to honor due process, and wish to use the vagueness in the law as a weapon against their political enemies. In the Soviet Union you could be considered "mentally ill" for opposing the state. We're already hearing echos of that now, here. You might be mentally ill if you're one of those "anti-government" types, you know, like most conservatives who oppose leftist government policies.
So nope, while it would be great to reduce the risk of psychotics getting guns, there is an even greater risk that good people will be denied their constitutional rights at the whim of their political enemies. Given a choice between those two risks, I'm inclined to believe there is more harm in the latter than the former.
Peace,
SR