Grant:
I suspect that the German high command sent Rommel to bolster the Italian defense and protect Germany’s flank in the Mediterranean. Allowing the allies to gain valuable ground, obviously would set the stage for an invasion of Italy, which Germany could ill afford with Italian forces capitulating during major engagements.
The actions of Rommel delayed allied invasion and eventual takeover of Italy by 9 to 12 months. This would’ve been enough had the Germans been able to reach Moscow in the original timeline.

Thanks for writing

Walter