I think this comes down to what the purpose of your reports are.
If someone does get injured, at my theatre, they fill out an accident report. (and plus, everyone was in the theatre. That is the official way to note an injury. Having been through the entire someone was injured thing going to court, I try very hard not to have multiple documents reporting the same incident. (If an accident report happened in a normal rehearsal or performance, I state someone was injured - a brief description - and then note that an accident report has been filled out. I have learned from past experience - I try not to have too much information on a report - due to privacy issues and the number of people who receive a production report. Also, if there is some conflict in two reports, that is a problem in a legal situation.
I think this totally depends on the situation you are working on. If I handed a report to the designer the next day, after they sat through tech, then tech notes, I think they would be a little pissed. (Trust me, just asking about something after tech notes, a side meeting, and a director talking to them - is enough to send them over the edge.)
BUT, I can see that there is a situation where Stage Management is the most senior person responsible for the show and you are going to want to document everything that was given in notes. If I anticipated an issue that may need to be documented, then I would start some sort of paper trails.
Unfortunately, there are times when you are working on a show that is just too large to be apart of every discussion after tech notes. For example, on my recent shows, stage management was in at 10:00a, teched from 12:00n - 12:00p - during dinner there was a 2 hour blood meeting, tech notes went to 1:00a, and then there was three different side meetings - not all of which I could attend, if I wanted to get the call done before 2:00a, and be back the next day at 10:00a.
Now, doing a short report that states this was our hours, this is what happened, this is what we covered, and then listing anything special that may have happened - with the note that tech notes were given directly may not be such a bad idea, but I am not sure I would do my full production report style. (Nor have I ever had a production manager ask,need, or expect a report during tech.)
It really depends on your situation and your style - remember stage management is an art and it comes down to the style that works best for you at the level you are working at.