Cathodes need to be hot in order to provide the function that they are supposed to perform. The getter flash on the glass envelope also benefits from some heat.
Outside of these, every other element in the tube only suffers from heat.
The main culprit is heat expansion of materials. This causes the elements to change their alignments when subjected to many heat cycles. Sometimes you can even hear thru the headphones a 'ping' sound of expanding metal when the tube is heating up. That's a element, such as a support rod for a grid or the plate, expanding from heat, and moving.
That's not good. The performance of the tube is highly contingent on the internal geometry. That's why "special quality" tubes have double mica supports to keep the electrodes firmly in place. Sometimes even tripla mica supports.
Some special material tubes (usually transmitting tubes) can get by without mica spacers. They also employ special glass that doesn't expand when subjected to heat; cleverly named Nonex glass.
That's another fail point; the glass - base pins seal. The pins are made of metal that expands at a different rate than the surrounding glass. When subjected to repeated heating and cooling, the seal is weakened, and some gasses get inside the tube. They bind to the elements and in time disrupt their operation.
Most tubes get by with passive open air cooling. Some military and industrial tubes can be reliably used in closed air for long times. Some transmitting triodes specify forced air cooling for reliable use.
Heat is the enemy of tube longevity. Since it is required for the cathode, it must be dealt with. However in no way would I recommend making the heat dissipation weaker.
The metal shields are for noise prevention in high gain circuits. Not needed in HIFI in most cases. The fact they hinder heat dissipation, is a necessary evil, it was never a feature.
