I can sort of see the Nazi invasion/occupation idea, but that doesn't work for how mesmerising and attractive the Tiger is - they are not petrified by it, they are a bit hypnotically entranced by it. So unless you are saying something about the erotics of the aggressor (which I'd rather Kerr wasn't) I don't think the Nazi parallel completely plays.
I think it's less rooted in specific historical circumstances than in a rather conventional fairy tale mode [qv Bettelheim]: Clever Polly and the Stupid Wolf is a sharper and funnier version of the same project: child - the epitome of defencelessness - (note here, exactly, the drippiness of the mother) faces Fiendish Danger and Is Able to See It Off. (The sort of intriguing thing about the Tiger is that in a way it sees itself off (once it has eaten everything) while the child just hangs fire. That's not very Nazi - the seeing itself off in due course. Oh, I suppose unless you are suggesting that if you're patient enough Nazism will blow itself out ... no, I don't think that's at all convincing, in context.)
See also the lovely Paper Bag Princess. [no passivity there]
And dd recently had from school a volume of rewritten Feminist Fairy Tales (Australian, they were) with lots of feist in them.
The other appeal is as a shaggy-dog catalogue story: first the sandwiches, then the buns, then the cake, then the tea, then the this, then the that; ... but it's OK there's still a café. I think the [food] catalogue aspect is one of the huge bits of appeal to children - hypnotic too. Maybe I have greedy children, but I think that's why they liked it - the grub. Mmm, perhaps the fantasy of being big enough to eat everything you think you want to eat?
(Oh and as for the blurb that says "delicious naughtiness" on the back, from Antonia whatsit - TOTALLY wrong.)