Our time is tracked per hour spent on project, not per work day - we are ETO.
You can record hours, just change global parameter.
And, we have production associates who can update status on each ticket so inaccurate hours wouldn't be an issue.
Sure it will not be so easy.
Same responsible can have several tickets on status "in progress" for same period.
I start working on ticket, set it in progress. Then receive urgent ticket, so open new one, to work on it and set it in progres : face to urgency, sure first ticket is still "in progress", so time recorded is doubled.
Also if ticket is opened (set to "in progress") by one user and closed (set "done") by different users, who is concidered to have done the job.
As I explained, it is not impossible, it is just "much more complex" than a simple difference between dates...