There are plenty of software projects, both FLOSS and proprietaty that aim to support people in this, mainly because many, many people need to keep track of their time.
On the other hand, each person's workflow and environment is different, so there probably is no one-size-fits-all solution for this sort of thing.
So, given that it is not an excessively complex problem, rolling your own is perfectly fine, I think. (Probably fun, too.)
But in my case, learning org-mode was faster than rolling my own. And of course, one doesn't need to use every bell and whistle.
On the other hand, each person's workflow and environment is different, so there probably is no one-size-fits-all solution for this sort of thing.
So, given that it is not an excessively complex problem, rolling your own is perfectly fine, I think. (Probably fun, too.)
But in my case, learning org-mode was faster than rolling my own. And of course, one doesn't need to use every bell and whistle.