I don't see how a lottery could benefit the player base as a whole, none of your examples actually work to support your arguments.

-The total pool of eligible people does not change between what we have now and your lottery. Its fine for you to say programming magic to filter out or prioritize people but in reality thats impossible to do fairly; a program can't see whats actually going on to be able to judge all edge cases and make an accurate assessment of who should be prioritized over someone else. So the only result from this is SE is unfairly picking who should have a house and who shouldn't. That is worse than what we currently have.

-The amount of time people have to get a house in your system would be set to 1 week. Currently we have as much time as we want to get a house and on some worlds there were houses left open after a week so you'd only be making it worse for them. Are you going to suggest treating players on one world differently than on others? That would be playing favorites and end up worse than what we have now.

-The current system gives players control over when and how they try to get a house. Your system removes that control and replaces it with RNG. This doesn't make for a better system for the players, removing control is a bad thing. Always. You can claim its still random if you get in or not but thats not true, it just appears so. You log in at X time, if there are Y people ahead of you then you wait your turn. its not a random number thats generated, thats competition for the same resource. A player still has control over when and how fast they try to log in to get a house. Just because the housing resource is limited it does not make it random if you get it.

-The claim that some players are at a disadvantage due to the time is irrelevant. Here's a couple pertinent facts to consider: 1 the maintenance patch must end at some point in time. 2. that time will be inconvenient for someone somewhere no matter what the time is. 3. Access to servers can't be staggered by time zone because multiple time zones can access the same server. 4. Because all times are equally valid in that scenario, you do the patch when your business is open. (this is the same for all patches, not just housing). 5. Players knew when this patch was going to hit weeks ago, they all had plenty of time to make arrangements to make sure they could log in if they chose to do so. 6. If players can't make time for it, thats not the fault of the developers and the developers are under no obligation to make changes for each special case.

-Your world has too much competition to get a house. This is a player created problem and your lottery system doesn't alleviate it in any way. it only changes it from log in to get a house to roll a die to get a house. Your odds of getting a house don't actually improve by having a week long lottery because you're still competing against everyone else that is in the market for a house. If anything it will lower your odds because those people who couldn't make time for the patch, can now buy into the lottery for it.

-Lotteries are not more fair than first come first serve. A lottery itself is a fair system for distribution but in this case you're removing players from being able to control when and how they try to get a house. See previous comments about that.

The ONLY thing your suggestion does is change when you try to get a house. It does not improve the system for anyone and would make it worse for some. You are trading the headache of waking up early to get the house with RNG to possibly get a house.