Further to the question on whether leaving it on to 13 or 14 degrees will damage the system, I very much doubt it, tho' how do these exponents ignore the FMS message 'TAI on above 10'?.
I don't have a copy of the MEL in front of me, but recall that if an engine antice valve is stuck or locked open, the operating limit is 38 degrees OAT. When one considers that you would only get such a high temp at or very close to the ground, the implication seems to be that even at takeoff power, no metal will melt.
This is not to condone deliberately exceeding any limits, tho' I did once have an argument with a sim instructor because he set up 11 degrees in 'fog' on the ground and I selected it on while taxying out (to see if it worked) because I figured we would be in 'ice' by the time the gear came up. Sure enough he had jammed the antice valve shut and was setting us up for a flameout and was right royally pissed off when I taxied the sim in for 'rectification' thus thwarting his rather obvious scenario.
Having said all that, the 10 degrees limit is probably conservative.
I know that I am guilty of forgetting to turn it on during climb until about 5 degrees, with no sign of any engine malfunction.