You are not looking far enough or hard enough. Granted, I easily run off to explore every 'what if' that comes to mind, but I do try to return to the basics.
Do you remember the story of Samuel, whom the Judge, Eli, took under his wing when Samuel was a very small child? Eli had two sons, Hophni and Phinehas, who didn't take the Law and customs too seriously. For example, no one was to eat until the fat sacrifice to God had been burned in its entirety. Then it was boiled meat they were to eat. Hophni and Phinehas would take raw meat and run off to roast it, because they preferred roast meat to boiled meat. They even ate their roast meat before the sacrifice had been completed.
We can see why people were thinking a king might be better than Judges. Samuel became a judge, and he had no better luck with his sons, and it appears (to me) that he also went looking for a young man he could take under his wing, one he could manage. He first chose Saul, who wasn't as malleable as Samuel may have hoped, so he went on a new search and found David.
Most Gentiles in these modern times, don't know, or perhaps don't remember, that the Judges were also the military leaders of their day. These Judges were, in effect, Generals, Priests, Prophets, Kings. It appears their children weren't all that interested in their heritage--and maybe not fit for it, either. Would a single king fare better? David did have Solomon...but his other sons...tsk-tsk.
Saul was a military leader, a tall man who is said to have stood a head and shoulders above others in his tribe. He had faced the cruelties of war; he had to give all to protect the eyes of men in a town that had been taken. He had seen and heard about all the Amalekites had done to Israel. Saul's was a message to the other tribes, that he would not stand for this continued behavior from the Amalekites.
I ponder the possibility that Samuel wanted to be the man, the power, behind the King. Easier to manage one man than an entire panel of Judges?
