Why was the Sanhedrin opposed to using the death penalty most times?
In Judaism, the purpose of Capital Punishment is not to punish the sinner, as punishment is by the Hand of Hashem, rather the purpose is to discourage others from sinning by showing them the severity of the sin through the severity of the consequence.
Therefore, if a beis din is using capital punishment often (e.g. more than once in 70 years), it's not so shocking for people and therefore no longer serves its purpose as a deterrent (therefore the death of the person is in vain and it is considered a murderous beis din).
This can be further seen from the fact that when capital punishment is carried out, e.g. stoning, the witnesses must throw the first stones because they were the most affected by the sin. (When one sees someone sinning it makes it less severe in his eyes), and therefore they need to see the severity of the consequence more than anyone else. (Michtav Me'eliyahu)
The Mishna, which contains the essence of the Oral Torah going back to Moses at Mt. Sinai, tells us that the Sanhedrin was supposed to sentence people to capital punishment extremely infrequently. See below:
A Sanhedrin that executes a transgressor once in seven years is characterized as a destructive tribunal. Since the Sanhedrin would subject the testimony to exacting scrutiny, it was extremely rare for a defendant to be executed. Rabbi Elazar ben Azarya says: This categorization applies to a Sanhedrin that executes a transgressor once in seventy years. Rabbi Tarfon and Rabbi Akiva say: If we had been members of the Sanhedrin, we would have conducted trials in a manner whereby no person would have ever been executed.