In thinking about Christ's passion and death, I haven't really spent much time pondering the suitability, if you will, of the specific means by which He died.
Crucifixion seems grisly enough to elicit compassion from sufferers and compunction from sinners, and it affords time for a few words that might profitably be spoken. The humiliation involved is a lesson for the disciple, on both what he can expect for himself and what perfect love really involves.
St. Thomas lists seven reasons "it was most fitting that Christ should suffer the death of the cross," four cribbed from St. Augustine: it was an example of fearlessness; at the Tree of Life, the New Adam atones for the Old Adam's sin at the Tree of Knowledge; being raised up, Christ sanctified the air; being raised up, Christ prepares for our ascent to heaven; the shape of the cross, and Christ's outstretched arms, signify the salvation of the whole world; a cross and a cruciform posture signify various virtues (good works, longanimity) and graces; and salvation is often associated with wooden rods and other objects in the Old Testament.
I recently came across yet another perspective on the suitability of crucifixion, among all the awful ways of death, being at the center of the Christian faith.
As then one who is crucified no longer has the power of moving or turning his limbs in any direction as he pleases, so we also ought to affix our wishes and desires -— not in accordance with what is pleasant and delightful to us now, but in accordance with the law of the Lord, where it constrains us.
And as he who is fastened to the wood of the cross no longer considers things present, nor thinks about his likings, nor is perplexed by anxiety and care for the morrow, nor disturbed by any desire of possession, nor inflamed by any pride or strife or rivalry, grieves not at present injuries, remembers not past ones, and while he is still breathing in the body considers that he is dead to all earthly things, sending the thoughts of his heart on before to that place whither he doubts not that he is shortly to come: so we also, when crucified by the fear of the Lord ought to be dead indeed to all these things....
In other words, crucifixion is an excellent image of the Christian life, since we live in this world still but find ourselves constrained in our actions and focused in our thoughts. (No doubt a lot of people also suppose living as a faithful disciple of Christ to be as enjoyable as being nailed to a tree.)
This thought reminds me of St. Catherine's observation that Jesus was fixed to the Cross, not by nails, but by His love for us. We, too, are held to our own crosses not by physical things, but by our own love for Him. We can (we do!) come down from our crosses at any time, simply by not loving God with all our hearts or our neighbor as ourselves. After a while, through the grace of God, we return.
I suppose it would be nice, in a way, to be held to the cross of Christian living by something stronger and more reliable than free will. If God is Love, though, then depending on our own love in response likely isn't a regrettable side-effect of an arbitrarily chosen means of salvation; it's kind of the only way that makes sense.