This is a very good question. The channel islands were fortified following a decision taken by Hitler himself in June 1941. He's on record as asking for maps of them and deciding to fortify them heavily and then viewing elaborate illustrations of the resulting fortifications. The resources used to do the fortifications were from Organisation Todt, not strictly speaking a military organization but a separate arm of the Nazi state. In other words, the decision to fortify the islands wasn't reached by military experts, but the political echelon of the Third Reich. Generally speaking, this is consistent with Hitler's strategic instinct to defend every bit of conquered territory rather than prioritizing essential areas to conserve forces.

But how much strategic importance should have been attached to the Channel Islands? The main reason the islands were indefensible for Britain in 1940 was that they are out of air cover from bases on the island of Britain. Without air cover, a naval presence is difficult to maintain, and without a naval presence the islands cannot be easily supplied or defended. In June 1941, the Third Reich was transitioning to the defense in the west, while preparing to shift the main theater of war to the east. Preventing the re-occupation of the islands prevented Britain from establishing fighter bases on the channel islands and forcing the Luftwaffe to devote fighter assets to containing this threat. So the Islands simply may have been more valuable to the German defenders in 1941 than they were to the British defenders in 1940.

By 1943-44 when the allies were planning a cross-channel attack, range limitations of fighter cover was an important consideration. Invasions west of Cherbourg were not seriously considered because not all of Allied fighter assets had enough range (P-47s and P-51s did, but other fighters did not.) The channel islands lie west of Cherbourg, so their role in the cross channel operation turned out to be minimal. However, the Germans were not necessarily aware of this either in 1941 or in 1944. They figured that a heavy occupation of the Channel islands would effectively protect the coastline behind it against invasion because heavy guns from the islands could reach the approaches to ports like St. Malo.

Ultimately fortifying the channel islands was very costly. Manpower was perhaps the worst example, since the Germans had approximately 30,000 troops on the islands in 1944 and these Soldiers effectively surrendered at the end of the war in 1945 without making any meaningful contributions.

To sum up, the costly decision to heavily man and fortify the channel islands was undertaken by Hitler and the political leadership of Nazi Germany rather than it's military leaders. They did it without a clear idea understanding of air-sea-land strategy in 1941-44. To be fair, this would have been a difficult thing to understand because of technological change and the unfamiliar complexity of such operations. German amphibious/air operations had been much smaller in scale than the Normandy invasion eventually became and they did not understand how easily the islands could be bypassed and the troop trapped. Lastly, the decision was characteristic of Hitler and Third Reich political leadership in it's reluctance to withdraw from overly exposed defensive sectors.