I think you (and several other people in the thread) missed the whole point of what the suggestion is. All those problems you mentioned are exactly why an actual lottery would be better, it's because it's already the same RNG. This doesn't introduce any more.
This would neither increase nor decrease anybody's chances of getting a house. Those would remain EXACTLY as they are with the current system. For every house that's available, one player or group will get it and the number who want it minus one will fail to get it, so your chance is determined by how many want it. The only thing that would change is how much effort and frustration it takes to get your (exactly equal to now) chance. If success is chosen by lot, then all you need to do is submit your name (along with the gil to prove you can pay for it) once, and wait for the result. No spamming the purchase hoping you can beat everyone else doing the same, no lost sleep, no worries about badly timed disconnects, no rush to be there the moment things open, etc.
That would be pointless, as your other characters would be competing against your main, not helping your main to get a house. Most people who want a house want it for the character or FC that they actually play. If you only want to go in and wander around your alt's house pretending it's yours, you can probably find a stranger's house where you can do that and save yourself the gil. Your main character wouldn't' be able to do anything with it besides hang out there either way.