if it's going to be random anyways..

[Penthea]

but still more merciful than what they have in place now.

That highly depends on the amount of competition. Entering a lottery would be near zero effort so the competition would inevitably rise. Dramatically so on some servers. You could also game the system by entering on multiple accounts. So while you would no longer have to placard spam, instead you could lose the lottery over and over again for months or even years.

Lottery would just swap one problem for another. Just like how the introduction of the placard spam swapped one problem for another. The root of the problem is the distribution of houses. Tackling this would fix availability issues. We need instanced housing or else there will always be a glaring problem with acquisition unfairly leaving out too many players.

Rng will never be a good answer to housing issues.