Replacing glass fuse with reset button fuse?
Power guy here. Nothing, and I mean not even the wildest circuit breaker, can act faster than a properly selected fast blow fuse - even the grid still uses them to avert catastrophic damage to the high tension lines.

Each output ideally would have its own protection that was tailored to the load characteristics for which it was being used. In any event, the input to the power supply should be fused, making your protection scheme downstream more flexible.

Thermal devices are based on current over time, and as such the delay should be predictable - should you be able to find a datasheet. But the delay, in most cases, will probably work out such that a 10 amp thermal element will blow soon enough that a 10 amp output channel wouldn't fail, provided the channel's absolute max ratings weren't exceeded. Personally, when I optimize things I like to oversize and derate when possible.

Now all you have to do is decide if the load you are powering will survive any delays in protective action. There can be a big difference between 20 amps for 1/1000th of a second and 20 amps for 1/16th of a second. If shorting is something you do frequently, maybe it's time for a current limiter.