1) You asked people for opinions and you got them. There was a clear consensus. If you wanted an explanation for it, you could have asked people to elaborate. Since you did not ask for elaboration, but instead decided to do what you wanted to do anyways, it looks like you were not really even open to considering alternatives.
2) A significant part of the explanation for the recommendations people give, particularly Jim Wendler, involves personal experience and decades of working with athletes at all levels. That experience, along with am understanding of the anatomy of the lift, tells people that the bench is improved by having strong shoulders of the sort built by the press. You can see that Jim has frequently recommended that people focus on the press when they want to improve their bench, as in these places:
"I also highly recommend learning to press and make it a priority in your training. ... You need strong shoulders to bench press and nothing fits the bill like the press." https://www.t-nation.com/training/virtual-bench-press-seminar
"2. Get Stronger Shoulders – this is especially true if you are a raw bench presser and need strength from the bottom. The Press is perfect for strengthening the shoulders."
"Make a commitment to getting strong shoulders. In other words, treat your standing press the same as you would any other major lift." https://www.t-nation.com/training/blood-and-chalk-2
"Military Press – I think this is so important that I use it as a core lift in my own training (and the 5/3/1 program). Strong shoulders are paramount for a strong raw bench press." https://www.t-nation.com/training/blood-and-chalk-3
Since, as you say, you are only pressing around 185, there is little reason to think that you have maxed out your shoulder strength and it seems plausible that keeping the press for that is wise. All of those links, by the way, include additional advice from Jim on improving the bench press.
3) If you have tried adding supplemental bench after the press, perhaps it is worth writing out in more detail what you have tried and what results you have gotten so that people can give you feedback most relevant to your situation. E.g., perhaps folk could recommend a set/rep scheme different from what you have done that might help, or a different exercise (such as a variation of the bench). Or, perhaps other issues are worth considering, like the need to build other muscles (e.g., see how much Jim recommends back work and curls in the links above), technique, gaining weight (a central recommendation of Jim's, and you do not seem far from "the small but painfully vocal segment of 155-pound T NATION readers" Jim imagines being adverse to gaining weight to help their bench), etc. Of course, you can also just ignore everyone, including Jim, and do whatever you think best, but then it really is a mystery why you asked in the first place (unless you were just hoping for affirmation of what you would do anyways). I hope other people who search the forums with your question are more open to learning from other, but wish you luck in your own attempts.