If your daily meetings are not working properly, do not look for solutions in articles all over the internet, you may be able to find them in the members of your team.
We are fortunate to work in such a heterogeneous environment that allows us to potentially work with people from all over the world, from the same country but with different culture, etc, and it is this environment the one that gives form to the routines in the team.
Whenever you put effort to make things right in terms of managing daily meetings, it is imperative that you open your mind and pick up practices that fit your awesome team. Below I am going to tell you what is working in the team I belong to, breaking a few myths-established rules that were not really working (context: full remote team):
"Stand-ups meeting should be very short, people should not be losing more than 10-15 minutes in it"
Look at the word "losing", if you really think that people are losing time when they are in a daily meeting then look deeper in your organisation to find the solution.
First: daily meetings should give value to the team, spending quality time in them is equal to winning time for later.
Second: daily meetings length is dictated by the own conversation, as long as everyone in it is satisfied with the result and had enough time to sneak-peak their topics.
Third: I like to think in daily meetings as a "regroup to study the next strategy and attack".
Sometimes it feels like daily meetings are a competition to enumerate tasks in progress or completed: "the more the better", but it is not. It is as simple as to visit JIRA project board to check the current status of the tasks.
The big point of daily meetings resides in being able to share ideas/thoughts/approaches with your colleagues. If you need to dig deeper in a topic with someone of your team, continue after the meeting.
"The SCRUM master/PO leads the meetings"
Why? I understand that someone could want to highlight something at the beginning of the meeting, but it could be anyone. Neither everyone must be in the meeting to begin with, it does not matter. What it does matter is that the meeting occurs, we are talking here about team culture and education, the meeting itself is bigger that anyone in the team.
"The daily meeting is enough to work the whole day without communicating with your colleagues"
Do not use a daily meeting to isolate yourself and avoid communication the whole day. As I said before, you could need to investigate further or do pair programming after a daily meeting, so you need to be able to coordinate with your colleagues in any or designate timetable, and also have the correct tools in hand to do such thing.
I just wanted to leave my reflexion and experience, so if you are eager to share your thoughts about this or felt that this post summoned you, feel free to comment.
Enjoy your meetings ;-)