Will "old style pyro wires" burn out?

My parents house was built in the 1970's. Pyro wires have been used and there is no 'ring main.' There are only isolator switches in place. The system seems sound and works well. We brought them an electric oven and there was no 'proper' way of wiring this into the main system. My father having spoke with an electrician friend said that it would be fine to plug into the wall socket and run as long as other things such as kettles, dryer, washing machine were not operated at the same time. So far my parents seem okay with the set up and I don't think there have been any concerns.

I of course got worried and consulted an independent electrician when they were not arround. The electrician told me that the entire house needed new wiring. He quoted, £5,000 for a 2 bedroom house but what got to me was when he said: "The pyro wires will eventually burn out if they keep using the oven like that, the system will just overload and catch fire and you will be lucky if you find anyone who wants to touch this wiring."

So will the pyro wires really give up? The wires look in good shape to me. They are not brittled, scuffed or falling apart in any way whatsoever.

Thanks.