I'll agree that the current housing system still isn't great, even if (in my opinion) 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.

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.