Precisely right. i especially agree and resonate with the part i boldfaced/ underlined, as that is exactly the purpose and how it is done today in the military, both in formal written orders and in informal email… I regularly correspond with individuals as individuals, and write to them just as i would a personal correspondence, but will often include others in the “cc:” line so that the cc: recipients will be quite aware of what i told/authorized/directed/approved the primary recipient to do, so that all parties will know that the primarily receipient is proceeding with my knowledge/authorization/approval/direction. And yes, i sometimes include certain details or clarifications in such “personal correspondence” that is strictly for the benefit of those in the “cc:” line, that i’d never include if it were a private correspondence to the individual. i think it more than obvious that is what is going on there
And @Vinnie 's protestations notwithstanding, if Paul was actually in fact writing primarily to the individual to whom the letter was addressed, to a close friend and professional colleague, then of course (contra Perrin et al) no thoughtful observer would expect Paul to use the “dramatic arguments, emotional outbursts, and the introduction of real or imaginary opponents and partners in dialogue”, rather than the “quiet meditative style”, even if he had hoped/intended/expected the letter to also (secondarily) be read by or to the entire congregation.
(In fact it just occured to me… if Paul was writing to Timothy, but with the secondary audience in view as per Fee’s analysis in order to bolster Timothy’s authority… then writing to Timothy with dramatic arguments, emotional outbursts and as an opponent in dialogue would have undermined his very purpose… as it would have appeared to the congregation that Timothy was getting what we call in the military a “dressing-down” from Paul, or cast Timothy as having an adversarial relationship with Paul in front of Timothy’s own congregation… this would have undermined Timothy’s authority in front of his own church, not bolstered it!)
Point is, if he did have that secondary audience in mind, then it makes perfect sense why Paul would still feel the need to offer some explanations, defenses, rational argumentation, or apparently unnecessary clarifications, even while the work as a whole is more characterized by the “quiet meditative style” that one would expect when writing to a friend and colleague.