Why does a fuse voltage rating only signify the dielectric strength?
To put it in another way, can I use a 1A @ 220V fuse in an environment
of 1A @ 5V?

Yes you can. It's the 1 amp rating that determines at what level of current the fuse initially melts.
However, if you used a 100 volt rated fuse on a 250 VAC application, then it may blow but continue to arc and conduct unsafely.