the TDA4605 will indeed blow the MOSFET if the chip is shorted internally. So it will drive full chip VCC into the MOSFET Gate putting it into full saturation which will make the FET go KERPLOW! Which it blows the fuse instead.
I am not too familiar with the Classic design, but I know power supplies and have rebuilt enough power supplies on various things to fill a house, and I know this to be fact...
Usually when a mosfet fails, it fails shorted through all 3 legs. Back to Gate. the microsecond it happens, it can send 160VDC B+ back into the drive pin of the chip just before it pops the fuse or causes other things to fail. if there is a Source resistor, and it opens, it will literally drive 160VDC B+ into the Drive pin all the time... But it usually wont pop the fuse. The fact that it keeps shorting the FET and popping the fuse, tells me the circuit path is complete on the Drain and Source pins.
Usually if there are passive components between the TDA and the Gate of the MOSFET, it will take those out. Sometimes... But not always.
Easiest way to rule the IC out is to leave the MOSFET out, and replace the fuse. Turn on the machine, and do a voltage check at the drive pin of the IC. if its pegged at VCC then yep... Otherwise, scope it and make sure the drive signal is within tolerance.
But experience tells me rule of thumb, when you change the MOSFET that suffered in the event of failure, you change its drive electronics too!
Given all of this, I still cannot rule out the possibility of the oscillator not running. if the oscillator doesnt run, and the state is pulled high, it can mimic the same thing assuming the small chance the drive IC is still good.
These days when I design electronics that need switching control, I usually try and capacitively-couple the output stage to the drive electronics with the appropriate pull-ups/pull-downs so in the event of oscillator failure or the loss of a specific regulated B supply, it doesn't blow the whole machine sky high.