It is possible to repair a plastic tanked rad.
The tanks are usually crimped to the end plate of the core, usually with a seal to ensure no leaks.
The cause of the failures could be vibration causing a fatigue type failure at weak areas. The pipes on the tank are connected to hoses that can hold them firmly enough to causie enough stress so the cracks to occur.
A Morgan does suffer more vibration than other cars(?).

thinking
As for cracking Al rads..... No need to wait for the noggin...get a drink, sit back......
The cracks will start from a stress point...these can be at joints, welds,bends etc.
Again vibration is a likely cause.
My Al rad had a weld failure where the top mounting bracket weld to the tank was cracking. The crack started at one end of the weld and was slowly extending through the weld.
It was due to poor line up of the bracket to the cross member causing side strain and a pull on the weld. Vibration will have then resulted in stress at the end of the weld.
The bracket was removed by letting the crack go most of the way along allowing easy separation.
Thorough cleaning and JB Weld stuck it back, the bolt hole was elongated to remove the side stress and a padded bracket added to assist steadying the tank. A new bobbin was also used.
No signs of problems over about 3k miles so far.

The Al alloy used for the rads is unlikely to be affected by heating to the temps of the coolant...poor welds are more likely causes or bad joints. Residual stresses can be left in welds unless annealed and vibrations aggravate these.
Blocks and heads get localized temps well in excess of a rad and this can lead to cracking, annealing can reduce this.
Different Al alloys are used for them but nothing exotic.
Blocks/ heads use casting Al alloy whilst rads use wrought alloys.
Hope that helps!
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Plus Four MY23 Furka Rouge