I think the reason is like Omar hinted the dual-nature of date-values which lead to the fact that your second load of the DateField didn't change the DateField from the first load - the numeric values behind the dates are the same and therefore no value will be stored and this means that also the string-representation (which contained the formatting) isn't touched.
The background to this is that Qlik doesn't store the tables like you load them (and how it the most other tools like SQL do) else they will be stored as symbol-tables (for each field one with only distinct field-values) and data-tables which contain only a pointer to the symbol-tables.
So if you really want to apply such logic of double-loading a field it should be rather in this way:
DateField as DateFieldOrigin,
Date (DateFieldOrigin) as DateField,
but if you don't want to keep the origin field I wouldn't use a two-step approach else just doing it within a single-step.