quote]GZ becomes vulnerable with aircraft losses and if it gets torpedo hits which reduces its speed. In other words it needs escort vessels, ideally Spahrkreuzer and Atlantic destroyers.[/quote]
I don´t think so. This is task force thinking, not raider thinking. Contrary to popular believe, a raider doesn´t need to be extremely well armed to be effective but fast and long legged raiders posing very serious risks. The one executing Sea controll needs to disperse forces to cover more areas but then is confronted with the problem to face a superior naval air force locally...
In a serious battle its not enough firepower and more importantly the GZ presents a large target that is vulnerable, in spite of all its armoured protection, to all types of opposing forces.
It only takes minor damage to put a lone raider in peril, and lead to its loss.
Agreed, and realistically spoken, the KM had to reckon with the eventual loss of a warship send out on a lone base performing merchant raiding. But this didn´t stopped the KM to do this, in fact, this is part of the raiding philosophy. The KM sent out a lone PBB three times (which can be trapped by multiple CL/CA or carrier or BC/fast BB´s), aven after the AGS sinking. They sent out HIPPER a couple of times, the twins, then BISMARCK with PE, despite the knowledge that neither HIPPER nor SCHEER on their own had enough firepower to conduct a serious battle.
The diificulty with this argument is that over time there will be losses of aircraft and pilots and an increasing risk of taking incidental and accumulating battled damage. To some extent supply ships can deal with this, but there will be a degrading.
Operational reserve was 50% for all airwing sizes given in german carrier designs with some planes in spares, some knocked down in parts. Losses will accumulate over the time, this is true but that´s to be factored in. Attacking a merchant is a low risk profile task (Fw-200 were quite effective in this). At one point GZ will need to return to bases in France or Norway as raiders normally do.
Please remember that speed isn't everything and doesn't necessarily give GZ complete security in the face of say night time attack by small surface warships such as destroyers. As soon as GZ starts to have its fighting capability degraded it becomes ever more vulnerable.
Also remember that GZ is as much likely to be in rough seas as in a dead flat calm. It won't always be able to fly off its aircraft which again is a vulnerability against small surface warships like a flotilla of destroyers in rough weather. Those 5.9 inch guns look good on paper - but they aren't enough especially against multiple targets.
I think here You overestimate the tactical usefulness of DD flottilla´s in poor weather. First of, in poor weather, that is weather poor enough to prohibit flight deck operations, a DD will be down in speed at a significantly higher penalty than a capital ship. Second, A flottilla of DD´s sound nice as convoi escort but in order to stop a raider continously running high speed (that is 26 to 32 kts) they lack endurance. They can´t keep up in poor weather and they burn fuel at very odd rates in high speed cruise mode or poor weather. DD´s typically have their most efficient speed at 12 to 15 kts while GZ´s was at 28. While a BENSON class DD burned only 1.25 ts/hour at cruise speed but gulped over 17 ts/ hour at battlespeed. A DD simply can´t track GZ for more than half a day before exposing the serious risk to run out of fuel. During the Bismarck episode and in the chase for Scheer, Hipper and the twins, DD flottillas frequently had to be detached from the main bodies to replenish fuel, let alone think of giving them an opportunity to conduct a night attack. This is a very serious burden in the tactical usefuleness of DD´s in the North Atlantic when trying to track a ship which needs to be located in the first place. The only case whe a DD flotilla were able to contact and attack a raider was in BISMARCK´s case, when Bismarck was slowed down and unable to steer. Even here their attack failed in making hits. The history of DD flotilla attacks against capital ships is a one sided story in both world wars, and I guess the KM considered 5.9in enough to inflict serious damage to a DD.
The basic problem remains, there are to many spots where a single raider can be in the ocean and the RN needs to commit and disperse very large assets to deal with that. Rumors of a single carrier operating somewhere between Greenland and the mid Atlantic is probably enough to paralyze shipping in the North Atlantic without even making contact with a merchant. Krancke successfully demonstrated what kind of impact a raider has on schedule of supply.