Surprised you've been to ANZ and didn't find their sockets best. Breakdown of things Type-I has:

1. small form factor – BS1363/EU no, US yes

2. grounding not required – BS1363 no, EU/US yes

3. good contact / not much wiggle (in type-I due to angling) – BS1363 yes, US/EU no

4. cable can either be parallel or perpendicular to the wall. You claim this is a failing but having options is good. Having a cable perpendicular to the wall is never an option with BS1363 and not having options is clearly worse (like with grounding) – BS1363/EU no, US yes

5. no risk of plugging in upside down – EU/BS1363 yes (BS because of required grounding), US no (need one pin to be larger which is error prone)

6. wall/female side can be flush – US/BS1363 yes, EU no

There is literally no downside to ANZ plugs imo. You say having required grounding is good but eh, many things don't need it. Even if we do think grounding is necessary, then the best option would still be type-I (because it is smaller then BS1363 and has the parallel/perpendicular options).

Schuko is terrible because needing a cavity in the wall in order to have good contact is a poor design and makes the plugs larger than necessary and I think that is the most important requirement.