There were many aristocratic sects among the 1'st century Jews living in close vicinity of the temple.
Apostle Paul was the director of the new Christian sect. Like all directors, his job was to hire the very best organizers, promoters, teachers etc. and dictate what is to be distributed.
The origin of Paul's evangelist's job was to eradicate all other monistic aristocratic sects in and around the region of the new Christian sect. Paul picked Timothy for this assignment.
Tim's main concern was not to denounce the Sadducees, Paul had junior apostles filling that role. The original role of Paul's evangelist was to eradicate and distort the history of any other sect.
Therefore, the term atheism rather than Sadduceeism. You see how conveniently the negative term seduce gets entered into the English language.