Which in turn has led to a large number of players with 'amnesia'. Makes me wonder why Lorax didn't include them as their own category in his census
All of the characters here have amnesia. If they're on this island, they have amnesia.
Quite decidedly incorrect.
First of all, every Toa, Matoran, or Turaga native to the island possesses their memories. And they never lost them, because as far as we know, Metru Nui never happened. Whether that changes or not is irrelevant; the only even possible memory loss is from the island change. Ignoring for a moment character-specific reasons, every being native to the island possesses their memories.
Second, not all beings from other islands forget. The Aitua, for instance, all remember their original home. They merely cannot go into much detail about it. Raknar remembers, and there are countless others I could list that remember where they came from. They merely do not talk about it.
This question was quite directly asked in the Q&A for the BZII. The answer was that they either had to forget, or not talk about it. That has stayed consistent, unless significant numbers of players are breaking the rules with their characters.