The use of fuses often springs from an FMEA (Failure Mode and Effect Analysis). You evaluate what the consequences of certain failures are, and how you can avoid them from turning into disasters. A failing component may cause a short-circuit, which in turn may lead to overheating, and eventually a fire.
A simple solution is to protect the device as a whole by placing a fuse even before the mains transformer, so that this is protected as well.
When I worked at Philips Audio we often would use PCB solderable fuses (a smaller version of these). They look a bit like small cylindrical capacitors. They have the advantage that electronics hobbyists won't go about replacing them; you have to recognize them as being fuses to begin with.
Why don't you want the fuse replaced? Most of the time there's a good reason why a fuse blows: some defective component. If you just replace the fuse and power the device again you may destroy more components, making the problem even worse and make a repair more costly.
While there are low-voltage fuses (like the PTH ones we used at Philips) you don't really need them. The voltage rating of a fuse refers to the separation when they're gone. You can perfectly use any 20x5mm glass fuse for lower voltage applications.