Your what if is ambiguous, are we taling Barbarossa (1941) or Case Blue (1942) ?.
In 1941 the Germans made a half harted effort against Crimea then opted to go for Rostov, in 1942 clearing out the Crimea was necessary to avoid having to leave a large force to screen the forces there.
Supplies could flow through Kerch so the Crimea would not be isolated until much of the Caucasus was under German control. Also the Soviet navy was much stronger than anything the axis had in the Black Sea, and with Sebastopol in soviet hands the axis needed to garrison a very long coast against brigade size landings the Soviets were capable of doing (and did a few times).
Leaving an Army and a strong fortress unengaged in their rear would require a large screening force, looking at what happened at the Odessa siege, and later south of Stalingrad even the whole Rumanian Army may not be enough.

In 1941 clearing the Crimea instead of pushing to Rostov, that they were unable to hold, made more sense in hindsight, screening the Crimea is more or less what they did.
In 1942 screening the Crimea would probably not make the AGS spearheads stronger, Von Manstein's 11th Army was flagged for an attack on Leningrad anyway not an AGS reinforcment. A better 1941 what if would be Von Manstein and the siege experienced 11th at Stalingrad instead of Von Paulus and 6th Army.