A lottery system wouldn't fix anything with housing though. If you're going to make changes to the housing system make changes that either fix or at least improve the system and its problems. A lottery does neither of these things.
Tenancy for example. If you fix the broken tenancy system to allow more tenants and grant equal rights to shared properties plus the ability to reset any demo timers associated with them. You stand to free up a decent number of plots as people will be a lot more willing to invest in and share a house with there friends as they'll all own it. So instead of having 4 or 5 people all owning 4 or 5 houses in 4 or 5 different wards and districts they'd be able to share 1 house between all of them and all have the security that goes with. Hell it might even bring the wards back to life if people are all congregating at the same houses instead of "oh hey I'm in the goblet but your in the lavender beds, Oh wheres Jack. Over there in mist..."
Under the present tenancy system though if the one guy who owns the house doesn't log on for a month everything tenants have invested and done with the house goes up in smoke! Even if they've been actively using the house every day... this is a huge fetterant to anyone that would happily share a house with there friends instead of everyone owning there own...
Another issue with housing is Gardening and Workshops. These could easily fixed simply by banging some allotments and a workshop in apartment complexes. Again likely to free up a good number of plots for other players given quite a fee people have empty houses they don't really want for no reason other than workshop access or a gardening plot.
Even a decent housing transfer system where players can easily sell trade or purchase houses other players no longer need... help friends move closer to each other. Like hey can I swap my plot 11 for your plot 41. Because my friends house is plot 42 and be cool to be neighbours. it's the exact same plot just ones in the sub division and one isn't. but if people could build neighbourhoods with there friends and stuff that could also breathe life into the emptiness that is the wards.
Or just allow people to sell off properties they no longer want. Instead of vacating it and sitting around for a month for the demo timer to offer you a fraction of its value and thus players think sod it I'll just keep it... especially when vacating it means you physically have to pull everything out of it which is a huge hassle for many people given the limited inventory space available.
Make changes that at least improve the system instead of changes that don't actually change anything.