As someone who has had relatives with dementia, from my perspective, even partial memory loss has a dramatic effect on personality.
Total narrative memory loss would result in death of personality.
The mode of expression (tone of voice etc) might remain the same but the person that was is lost forever (the person that emerges after, if they can, might be considered by some a better person but it's not the same person).
That is a human being.
The mechanics of droids minds aren't explained in the story.
We know the droids stay in character when humans aren't listening or when they think they are on their own and continue a private narrative but that might be just a quirk of programming.
In terms of the audience that isn't as important as their position as characters.
We are meant to care about the droids (which carry most of the first film and play a pivotal role in the whole of the OT) in the same way as the other characters.
They are our point of view or witness for the majority of the time.
So in terms of making the PT work it's necessary to return to that way of addressing those characters.
I'm not arguing that they should carry the story (though it might have been a good idea if we were starting from scratch).
But the audience should see them as real characters that worry and feel fear, pain etc (even if mechanically they don't and the rest of the characters don't believe it).
When Owen casually insists that Luke has Artoo's memory wiped he is casually insisting that the little guy we have already come to be interested and endeared to be killed.
He is a slave, his memories are inconvenient to his owner.
If a human did that to another human it would be seen as inhuman and yet we, the audience are meant to both empathise with Artoo and simultaneously recognise that Owen doesn't see Artoo as a human (even though we are encouraged to do so).
This is an example of Lucas not understanding how his own work worked.
Star Wars (1977) is more narratively complex than he realises.
Having Artoo laugh his nuts off at Threepio having his mind wiped is a total inversion of the character, it turns him into a evil sod.