How secure was Germany's last foothold in the Caucasus in 1943?

Good defensive position but nothing much else

Although Germans painted Kuban bridgehead as a bridgehead, i.e. the place from which they could start a new offensive into Caucasus, reality on the ground was somewhat different.

First of all, geographically speaking area is divided into three parts by Caucasus mountains themselves. You have northern part which is relatively flat, mountains themselves and coastal region in the South. Northern plains were in 1942 object of German advance with their motorized forces. However, as Soviets gradually outnumbered German armored formations, this area had to be reduced to relatively narrow front that could be defended with fortifications, anti-tank guns, system of trenches etc... Mountainous area was never good for offensive operations, as Germans witnessed in 1942. However, now it gave them solid foothold for defensive operations. Finally, on the coast Germans never advanced much further from Novorossiysk even in 1942. Now they wanted to hold this port, to deny it to Black Sea Fleet, but any offensive operations were pretty much unrealistic, as Germans did not posses naval superiority or troops and means for large scale landing operations. In reality, main strategic benefit for the Germans was purely defensive one - to protect Crimean peninsula further to the west.

To further proof this point, it should be noted that only panzer division in Kuban bridgehead was 13th Panzer Division, and even they were withdrawn and reassigned in May of 1943. Rest of the troops in German 17th Army were either regular infantry or mountain (Jäger) divisions. Supply of these units was done from Crimea across Kerch strait. Kerch strait is only 4-5km wide at narrowest point, and appears it was not that critical. Germans used all kinds of barges, ferries, local small craft and even built a railway bridge (not finished but useful as it had railway connection) and a cable car to cross this relatively small obstacle. Capacity of the cable car was estimated as 1000 tones daily. Overall, Axis in general had abundance of suitable vessels for transport, as even Croats (smallest Axis contingent) had at their disposals dozens of vessels which could make several ferry runs daily (and nightly) across the strait. Soviet naval forces could not intervene while Luftwaffe had aerial superiority over the Crimea and overall that part of the Black Sea. Therefore, major part of the fighting over Kuban were aerial battles, and precisely in this sector of the front VVS for the first time managed to wrestle control of the skies on their own, i.e. without ground forces advancing and chasing of Luftwaffe units.

As for fighting in Kuban bridgehead, it could be described as bloody but without much gains, especially if we consider early fighting in the spring of 1943. Soviet landings which were mostly unsuccessful except one at Malaya Zemlya, then subsequent Germans attempts to dislodge them in Operation Neptune etc ..Soviet attacks continued during the summer but without much success. However, situation in other parts of the front became critical for the Germans after their Kursk offensive (Zitadelle ) failed to meet its objectives and subsequent Soviet advances all across the front.

In any case, Germans decided to withdraw from Taman peninsula already in early September of 1943. Soviet operation to liberate Novorossiysk which lasted from 10-16 September 1943 only sped up German preparations for withdrawal from Taman peninsula (Operation Kriemhild) .Kriemhild was done relatively successfully as German troops hopped from one defensive position to another until vast majority of them crossed over to Crimea. However, as mentioned before, relatively narrow Kerch strait now proved a hinderance. In November 1943, land connection of Crimea in the north was cut off and at the same time Soviets launched Kerch–Eltigen operation on the eastern side of the peninsula. While costly, this operation forced Germans to divert part of their forces to the east, thus dividing them to two fronts which ultimately doomed their defense when final operation for liberation of Crimean peninsula started in April of 1944.

What would be a final assessment of German supply situation considering Kuban bridgehead ? At first glance, if the supplies were available in Crimea they could be brought to Taman peninsula with relative ease. In most of the 1943 Crimea had land connection with rest of German forces, as well as supply directly form Romania cross Black Sea. Theoretically, if they supplied 400 000 men in infantry divisions, they could have supplied similar number of troops in panzer divisions. Usually panzer divisions need more supplies (especially fuel) do to the armor and other mechanization, however, there is no proof that transport system over Kerch strait was a bottleneck, not even during the retreat in October of 1943. In reality, neither the Germans had the strength to launch another invasion of Caucasus, nor was Kuban bridgehead good place too start such invasion do to geography as explained above. Germans planned for 1943 to be a defensive year, with one large offensive around Kursk, not to gain some strategic objective (Kursk was not that important) but to lure and destroy Soviet armored reserves, thus preventing their offensive usage. In any case, when that failed and Soviets started rolling westwards, whole Crimean position became untenable. Kuban bridgehead was just a part of the problem, because with severed land connections now everything depended on transport across the Black Sea under increased Soviet aerial and naval activity.