You're assuming that everyone's schedule follows the sun the same way. People already have different time of availability because of sleep schedules. Without time zones you wouldn't have to do the additional step of converting times or asking their time zone or being caught off guard because you didn't know their country went to DST already.

'Are you available between 10 and 16?' vs 'Are you busy tomorrow morning? oh tomorrow morning my time, uh like in 10 hours'