But the thermal fuse will blow, long before the transformer catches fire.
If there is a short on the other side, it may catch fire before temperature of the transformer rises sufficiently to trigger thermal fuse by overheating.
I don't understand what you try to say but here it is:
1. Transformer won't catch fire before thermal fuse cuts primary current... Thermal fuse will cut at 100-120°C. It is inside windings. There is no fire at those temps.
2. Electronics on secondary side of transformer must have their own current/thermal protection. It can catch fire at any time without taking trafo or any of it's fuses out of their specs for normal work.
3. Primary side current fuse protects power socket and household installation from short circuit. Not transformer. That thing is long gone if it is in short circuit.
4. Your household power sockets should not be connected to 25A fuses. 6A and 10A and 16A are ok if sockets are made for that current. They cannot be damaged with that. Smaller fuse on you trafo primary is good practice, because if done right, it might cut before your distribution box one, and prevent blackout for other devices connected to same circuit. But it doesn't protect your socket and distribution circuit. Your distribution circuit has to be designed to be protected on it's own. Otherwise it is not done properly.
5. If you want to have protection from both thermal and all kind of overcurrent protection, you need to have thermal cutout, primary fuse (for short circuits) and secondary fuse (for overcurrent on secondary side). Thermal cutout will handle defects where current rises so much it doesn't blow any of the fuses but is still overheating trafo.
6. Trafo insulation is specified for working temperature. There is such thing as max permissible working temp, max peak short term working temp, and permanently damaging temperature. If you reach that one, your trafo is permanently damaged, and must not be used anymore. Because of that, standards prescribe that a one time blow thermal protection element be put inside transformer winding, in such a manner that it cannot be replaced without damaging it completely.
It is deliberate kill switch. Resettable one is strictly forbidden for that purpose.
User or manufacturer are free to add additional resettable thermal protection element, set for max peak short term working temp, to protect transformer from occasional incidental overheating from user pulling marginally higher current from nominal, or when there are chances of working in extreme heat environments. Also it can be used to protect equipment specified for periodic intermittent work that is supposed to work short period and that should let certain period of time to cool down...
With small transformers, most of the time resettable one is not used, but trafo is simply slightly over specified, and core is run at lower power density so trafo has reserve..