The example (which is not so uncommon) that an appointment is set in timezone X, author of the service storing the appointment helpfully converts to UTC, timezone of the originating country changes and then the "return" from UTC to source timezone is incorrect, because now UTC-0600 is actually UTC-0700.
In short, any conversion that reduces precision is flawed. Dropping timezones after normalizing them to a canonical format makes it impossible to restore the conversion.