The problem I have with the current system is it gives an advantage to people using autoclicker addons and it encourages people to farm for hours on end for a small chance at being the first one.
A lottery system would give people a fair share at it without encouraging people to sit there for hours not knowing when the timer will come off and won't give you an advantage if you use an addon.
I really see no downside to using a lottery system, and this is coming from someone who already owns a house.