Blame the limited houses, not the lottery system! It takes that long because of a serious lack of houses. Dont expect that a shorter cycle gives better chances on that either, since there will simply be more cycles in which no houses will be available at all.
That each bid only has 1% is because of a big lack of houses. With 5x as high of a supply, this would become closer to 5%. The lottery scales almost linear on that (only when nearing the 100% this doesnt work anymore since at that point people will start bidding in such way that location becomes a factor.
Lets look at the odds at a 5% winrate and the number of cycles needed there. And for convenience, lets start at 20 cycles: 64.2% win chance (vs 63.3% of the 100x1% rate). And for reference after 100 cycles at 5%: 99.4%.
Now lets say the supply is equal to the player base, location will matter. And as a result some plots get no bids, while some get 5 bids. You will still have to face the randomness here (20% winrate), and again, more of these opportunities means a higher chance of obtaining it. It doesnt matter what state we are in, it works, and it works in a fair way.
Thats why the lottery is good. It scales in the best way with demand vs supply. Its that the supply is currently not even close to what is required.
Again, dont blame the lottery on this, blame the lack of wards. Because the lack of wards is what is garbage here.