Scrum is defined by the Scrum GuideScrum Guide, which says, among other things, the following about the daily scrum:
The Daily Scrum is a 15-minute time-boxed event for the Development Team
The Development Team uses the Daily Scrum to inspect progress toward the Sprint Goal and to inspect how progress is trending toward completing the work in the Sprint Backlog
The structure of the meeting is set by the Development Team and can be conducted in different ways if it focuses on progress toward the Sprint Goal
That is, how a scrum team tracks progress towards the sprint goal is up to the team. If you feel a different way of tracking progress is better, discuss this with the rest of your team during the next retrospective.
PS: I get the impression that the flexibility and team autonomy of scrum is news to your team. If so, I recommend that everyone attend a scrum training, or at least take the time to read the Scrum Guide. In my experience, the Scrum Team must understand Scrum to use it well.