This forum and others have a lot of bad information on how a modern proportional inertia brake controller such as the popular Prodigy P2 and P3 works.
These controllers are not zombies. They are in fact very sophisticated computer controlled devices that work very well.
The controller will very the current output to the trailer dependent on the amount of deceleration the controllers inertia detector sees. This is the feedback the controller gets.
With a sound trailer brake system that can be set up as per the manufacture's instructions that does not require maximum gain it will not make any difference if the trailer wiring is 14 gauge or 10 gauge. The gain setting basically makes this compensation.
The overall maximum current seen with 12 volts at the brake magnets
is about 12 amps. 14 gauge wire can more than handle 12 amps.
As for the wiring becoming a fuse the Prodigy controller will not output more than the gain setting even with a dead short. This would be about 12 amps with a maximum gain setting which a 14 gauge wire can handle continuously.
Bottom line if you want to rewire with 10 gauge do so. If you are going to rewire the trailer I still suggest a separate run for each side and eliminate the troubled wiring in the axle tubes.
But if you are having brake problems 10 gauge wire may not correct the problem. There are many more factors that need to be considered first.