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I've thought about repairing cracks in tubing by filling the tube with something like epoxy or a melted polymer.

The substance would have to have the right strength and rigidity.
For smaller diameter tubes the "resin" could be high-density, whereas for a large-diameter tube it could be dispensed as a foam, with some volume percentage of air.

I've used engineering resins for "potting" of electrical circuits, both for vibration resistance and water exclusion. The resins can be custom-tailored to the customer's needs.

Unfortunately, there seems to be no data on what has worked for a bicycle frame.

Also, any bandage-type repair has to take into consideration the possibility of excessive stress concentration where the bandage ends and the original structure takes over, so the repair material has to have flexibility via some combination of material properties and tapering of the thickness. Lastly, some degree of bond adhesion would likely also be a factor in any such repair's durability.

Overall then, designing a repair is more complicated than it first seems. Doubly so in the case of high-performance (i.e. lightweight) structures.