That perception is based on 15 years of field and workshop service experience backed up with engineering qualifications, 35 years electronic design experience and the recommendations of several AS and IEC standards...

Standard AS/NZS 61558.2.6 is but one example.

The main issue here is inrush currents. A (conventional) fuse needs to be able to survive a 2x rated current for a short period. Problem is. such a fuse will suffer from repetitive thermal stress and eventually fail from metal fatigue. So there is an inevitable tradeoff between safety and reliability.

Many common fault conditions will result in currents that will not cause a secondary fuse to fail but will, over a few hours, heat the transformer sufficiently to cause catastrophic failure. Then, if you are lucky, the primary fuse will open.

Another common fault condition that will cook a transformer due to core saturation without obvious external symptoms is an open circuit diode in a bridge or full-wave rectifier. There is no over current condition here, only a thermal fuse will save you.

Fusible resistors are generally a better choice for when you can't readily trip the power off with over-temperature.

I agree with you, too many fools just fit a bigger fuse so "it won't blow again". I know of at least one house that burned down when a 10 amp fuse was fitted in place of a 1.5 amp slo-blo. And, on a larger scale, a substation at Pymble that went up in spectacular fashion for a similar reason!