I don't know. I'm sure it would happen quite a lot, but some commanders may well see this sort of thing as a mistake.
The Germans were guilty of cherry-picking talent from the fittest new recruits and the Wermacht for the Waffen SS, to the detriment of the regular army. To extent, this practice was repeated for Goerring's pet Luftwaffe field divisions. Waffen SS units could be counted on, for the most part, to fight competently and with vigor, but the regular army suffered qualitatively for it. Quite a few military historians have noted this as being a serious strategic error on the part of the Germans. If they'd spread the cream a little more evenly, the army as a whole would likely have been more effective. It was usually regular Wermacht units that buckled under attack, and it was often the Waffen SS sent to plug up the gaps. I believe the applicable idiom here is "borrowing from Peter to pay Paul".
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