Hmm, not true in my experience. Family members have insurance paid psychiatric care and got their first appointments within a couple of weeks. I get that this is variable in different areas and insurance plans, but you stated no insurance and 3-6 months wait as general facts. That is incorrect.
Definitely variable - I am in Seattle and this is the state of affairs. When I was in NYC the same or worse. In WA state there are effectively zero in patient beds to the extent people in crisis are warehoused in ERs or jail. Where are you? Not specifically about wait time, curious where you rank. My experience in WA and NY ranks 11 and 15 in the US, so most Americans fare worse:
