In response to the initial question, my default note is "No notes, thanks" to each of the departments, and "Nothing to report" in the Absent/Late/Illness-type section, since it is not addressed to anyone.
I think the culture of theatre that I have been immersed in, "Please" and "Thank You" are almost like punctuation. Even to the point that rather than calling "Hold" in tech, I usually end up calling a "Thank you, hold please!" To me I think it stems from the "Thank you, five" style acknowledgements we so often get. I've heard actors saying thank you as a way of acknowledging they understand a director's note. "Thanks" is also almost a default email closing for many people I interact with. Even yesterday I got an email from wardrobe saying they fixed a costume piece, and the email was signed with a "Thanks!" Are they thanking me for asking them to fix the costume? Thanking me for reading the email?
In a "No notes, thanks" situation, to me it's me saying "Thank you for reading," or even "Everything is good, thank you for contributing." I do try to say "Thank You for..." when we recieve new props in rehearsal, as a way of acknowledging our receipt and indicating the prop suits our needs. Otherwise, there's a separate note about what should be changed about the prop, and usually those include a "Please." If a note was addressed in the run, I may simply state that something was fixed, but occasionally I do say thank you in a performance report.
Maybe this is all because I am a younger SM and make up for my lack of klout with politeness. But I find with the people who I work with on a daily basis I do need to infuse the extra "Please" and "Thank you" to keep things friendly, and to get results, but that may be a unique wrinkle of how my theater works.
Beyond that, to me, "Please" does not have the inferred meaning of "Do this, if it pleases you." It's a signal that something is needed. I say "please" to an ASM, even if they need to do something whether it pleases them or not. In the same way, "Thank You" doesn't carry the meaning of "You are so gracious in doing this for me, who is unworthy." It's a closing of the loop opened with please. An acknowledgement that I am satisfied, that the outstanding need as been fulfilled. And ultimately thanking the person for their time and interaction, because even if it's someone's job to do something for you, I believe you should still thank them for it.