As is the fining pot for silver, and the furnace for gold, so the Lord trieth the hearts.
Proverbs 17:3 GNV
Doeg, the Edomite, a high ranking official for King Saul as such had no personal vendetta stated against David, but also had no inhabitions against murdering the Lord's priests. The Ziffims were loyal to King Saul as well having no qualms about letting the king know where David, his family, his men were. Its one thing to move around by yourself and keep hidden. It's totally different with two wives, Dad, Mom, brothers and sisters, maybe an uncle, aunt or two, and then add about 600 men with their families who were also in dire straits. Then there's an exchange or two with the Philistines in Gath. And Saul sending men to take David out of his own home, out of his own bed! Did Jesus have these same encounters? Not at all. Did Jesus face some who were "loyal" subjects, but not to Him?
When Jesus called Lazarus from the grave...
Then many of the Jews, which came to Mary, and had seen the things, which Jesus did, believed in him. But some of them went their way to the Pharisees, and told them what things Jesus had done.
John 11:45 - 46 GNV
To address various individual situations Jesus told the disciples the night before He went to the cross:
If the world hate you, ye know that it hated me before you. If ye were of the world, the world would love his own: but because ye are not of the world, but I have chosen you out of the world, therefore the world hateth you. Remember the word that I said unto you, The servant is not greater then his master. If they have persecuted me, they will persecute you also: if they have kept my word, they will also keep yours. But all these things will they do unto you for my Name's sake, because they have not known him that sent me. If I had not come and spoken unto them, they should not have had sin: but now have they no cloke for their sin. He that hateth me, hateth my Father also. If I had not done works among them which none other man did, they had not had sin: but now have they both seen, and have hated both me, and my Father. But it is that the word might be fulfilled, that is written in their Law They hated me without a cause.
John 15:18 - 25 GNV
Each of these psalms represent a personal afront, literally life and death, and for some others definitely death, for the individual writers.
Because these psalms are very individualized in reaching out to God for the strength and power that alone are God's of course Jesus didn't pray these specific psalms. Even so Jesus faced personal situations which no one else could pray the prayers He prayed. But looking to His Father of a certainty He desired the strength from His Father to face the person or situation. What were these situations that Jesus needed strength to face? His cousin John the Baptist was executed for Jesus' sake. His own home synagogue wanted to kill Him. Different ones He healed being questioned by the Sanhedrin as both the healing (on the Sabbath) and the following instructions (take up your bed and walk) were against the traditions and rules held in high esteem among the Pharisees and Jewish leaders. Jesus did indeed face the trials and pressures these psalm writers encountered, and as man He knew in His situation the reality of what they faced against personal adversaries. The prayers of the writers of these psalms and others were indeed a pattern Jesus could have followed in His times of His communing with His Father.