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Keep in mind that real world computers just have a very large (but not unbounded) amount of tape. Since they have constant space, they are really just DFAs.
Well... sizeof of an expression is mostly useful for not repeating yourself in cases when you need the size of a type you already have some way of referencing, as in
a = malloc(sizeof(*a));
It's also useful for various hacks (stuff like compile-time assert macros), since it doesn't evaluate the expression, only its type.