There was a discussion on this forum some months ago about whether 6mm was inadequate for modern showers. The question was asked if anyone had come across a shower supply cable that had suffered damage from overheating and no one had. The consensus was, was that the switchgear was the issue regarding overheating.
While the situation with ever increasing wattages needs to be addressed it must also be recoqnized that a 6mm cable clipped direct is rated to carry 46 amps continuously (24 hrs) That means it will carry 46amps for a half hour without registering any or little heat to hand touch.
My shower (in a rented house) is a Triton T90 (8.5 kW). It's wired in 4mm. We like our showers. Inspected the cable every year. It's in perfect nick.
Is it possible the particular 6 mm was of anon standard variety.? I have come across T&E that was hard to strip not because of overheating but due to poor quality?