Is it wrong to use the statement, ‘God died on the cross’?

This text is from a letter written by David Gooding in 2003.

As far as I know, Scripture nowhere says that God died on the cross. On the other hand, it is true to say that he who died on the cross was God. To put it another way, it would be quite wrong to say that the Father died on the cross; but perfectly true to say that the Son of God died on the cross (Galatians 2:20).

Moreover, the Son of God who died on the cross was, from all eternity, the Word of God who was with God, and was God. He subsequently became flesh, without ceasing to be God (John 1:1, 14), and he died for us on the cross.

Why Scripture does not anywhere say that God died on the cross is because the term 'God' implies the Father, as well as the Son, as well as the Holy Spirit. To say baldly that God died on the cross would be equivalent to saying that the Father, the Son, and the Holy Spirit all died on the cross, which would not be true.

With warmest greetings,