So, I recently watched Infinity War/Endgame for the first time. And it brought to mind a lot of the complaints I see around Discovery about the crew, always encouraging each other, showing support, etc. And I had to laugh because that's a huge part of the Marvel films. You have the constant reassurance this going to work, little quips and asides during critical moments of encouragement, and overall providing emotional support.
And I realized that it isn't that Trek is doing something wrong; they are doing exactly where culture is at right now. We no longer live in a world of TNG, where yelling at a subordinate is considered good leadership. We live in a culture which requires emotional reassurance and support, and that is reflected in the art being made.
So, no, I don't see the crying stopping or the counseling being needed. I see it as reflective of the culture and the day and age. If it is bothersome, then this show may not be for the individual. Because it sure as hell ain't going anywhere.