Thank you for highlighting this issue. Suicide leaves a gaping hole for everyone - just as the person who died by suicide was facing an insurmountably gaping hole without enough support.
You've talked a lot about psychiatrists - and psychiatrists offer a certain type of care that is beneficial to many. But far from all.
We need to embrace a wide variety of treatments for people who are suicidal. This includes psychiatry. And also traditional talk therapy, which is generally more readily available.
But we also need to fund as a matter of course other therapies: art therapy, farm & animal/equine therapy, spiritual/religious-based approaches.
Treatment should be tailored to an individual's needs, not a line entry on an insurance form.