No, it doesn't work like that. You have to breed for many generations, and cull hard, in order to fix "type" in a crossbred strain.
First crosses, on the other hand, are very consistent and predictable. We see it all the time in livestock breeding. (And plant breeding too, I believe).
Basically, if the parents are 100% purebred the outcome of the cross will be predictable. Subsequent crosses between crossbred parents involve an ever increasing number of variables, and are not predictable.
Look at how consistent these sheep are. Like peas in a pod. Thousands of them. All first cross. The most popular commercial type of breeding ewe in the UK:
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