Almost ANY system would be better than what we have now. Also, adding Ishgard or 20 new wards to existing districts will only postpone, but not solve the systematic failure of soulless placard clickery.
This particular idea can be slightly improved, methinks. I would add something like:
When you aim for a plot, wait all the time and DON'T get it, you recieve an 1x "housing tomestone", which slightly increases your chances in RNG roulette next time. The more previous attempts - the more tomestones - the more chances to get your house in a next attempt.
This way, you are rewarded for efforts of wishing and hunting for house for a long time. And even if you don't get it again and again, you still retain a little sense of accomplishment, since you can see that you're working towards it.
+, Of course, 1 house per account.