It is unfortunate that there is some damage to the heating cable.
it is absolutely not advisable to just remove the earth connection.
- anyone who was to work on the circuit in question could be in danger due to a LIVE (earth connection)
- the earth cable in the heating tape will be surrounded by ground (levelling compound, concrete etc) it will act like a grid and try to bring that section of floor up to 230v. it will be reduced voltage due to contact with the surrounding ground.
- there will be a constant current flow from live to earth that will increase your electricity bill.
- voltage of your floor will vary depending on many factors outside your control. ground water level, humidity, cracking or other damage to floor or substrate, salinity, spillages etc.
- if the circuit is supplied via an rcd or rcbo, it will cause nuisance tripping anyway as there will be times when there is enough current flow to real earth to trip the device. If it is not rcd protected, then see below.
- it is quite feasible that one evening, maybe many years from now when the conditions are just right, your wife, child or grandchild will get up in the night, walk in with bare feet and turn the tap on for a glass of water. By holding the well bonded tap and standing on the faulty floor they make the circuit complete and you have to come down to find them dead on the floor in the morning.
Thankfully,
I am one of the majority of electricians that has never had to explain myself to a coroners court or a family of the deceased. I don't know what would be worse but I
hope, ensure by good morels and working practices that I am never in that position.
You say your idea is a bit controversial, I am amazed that you have not been hammered for even suggesting it.
you have your profile hidden so I don't know your electrical skill set,
if you are a professional electrician SHAME ON YOU
if you are a diy guy
Please look at what I have written above, whatever expense and/or inconvenience is incurred, is not important. we all screw up every now and then. its how we deal with it that makes us who we are.
Bottom Line, your options are.
1.. rip the floor up and do it again, this time get it right.
2...cut the cables off where they enter the ground, put a radiator on the wall.
3....SAVE MONEY AT THE EXPENSE OF PEOPLES SAFETY.