Further to this its not likely to result in less children being abused.

If you have the death penalty for even possessing CSAM as the parent suggests, then there is no incentive to not get into distribution or even actively abusing children and producing CSAM once you posess some. The punishment isnt any worse so why not? Its the same reason for proportionality in other crimes, we dont punish robbing a bank with life in jail as then there would be no reason for anyone who robs a bank to not just murder everyone to leave no witnessess.