I'll agree that the current housing system still isn't great, even if it's much better than it was before.

That said, I don't think your proposal makes it much better; it simply adjusts the system so that it's weighted a bit more towards a long-term "first come, first serve". Such a system would discourage newcomers from engaging with the system, as they would feel like they are at a disadvantage relative to those who have been trying longer. Personally, I don't think that's desirable; you want a lottery like this to feel as fair as possible to everyone who applies.

Regardless, this proposed system also has the same problem as the old one: you're still at the whims of probability, meaning it's still entirely possible that even with more entries, you will never get a house. It's less likely, but still possible, and with so many players that means it will happen to some people.

At the core, the improvements to this issue shouldn't be one of deciding who most deserves to get a house; rather, it should be recognizing that the demand outweighs the supply, and doing what's possible to increase the supply to meet the demand.