Why A fuse is chosen to protect the wiring and the device, not the fuse itself. It should open before the current exceeds what the conductors and components can safely carry. Putting in a 20 A fuse where a 5 A fuse belongs lets up to four times the rated current flow through wiring sized for 5 A, so the wire or component can overheat and start a fire before the fuse ever opens.
Watch out The idea that the bigger fuse blows more easily reverses the rating: a higher amperage rating means it takes more current to melt it, so it blows less readily, which is exactly the problem.
The fuse protects the wire, not the fuse. Never fit a fuse bigger than the circuit is rated for.