A 3 year waitlist would be short at this point. Often it's 5+ years, or they close the waitlist for a year or two, only opening it up for a brief window, and then they'll tell you that that advertised 5 years is closer to 7. It varies from area to area, and a lot of people don't seem to understand that. It's not as easy as they seem to think, and if you have to move due to poverty and needing to find something cheaper, you might move out of the area you applied in, so you get to apply and get to the back of the next waitlist.
Housing is a human right, and we need to start treating it as such, not as a fucking commodity/investment.
