Depends on what you need.

If you specifically only care about moments in time, throwing away the input time zone might be fine.

If the application is more human centric, timezones are often very useful as humans move around but often think about time as timezone-relative. A log of your daily activities would be confusing if a past event logged as 09:16:01 suddenly showed up as 07:16:01 because you're travelling when viewing it.