As a result, there were people that worked 6am to 3pm(ish), 10-3, followed by 7-10 in the evening, 11-8, etc. I had a young child and handled school dropoff, so my hours were roughly 9am - 6pm. My boss, the CEO, was a workaholic who arrived around 10am and worked to whenever. I spent an amazing amount of time dealing with "where is everyone?" sorts of questions, despite the team running fairly efficiently and still completing work on aggressive schedules.
The solution was literally “come in any time you want as long as your projects get done” - what’s your objection? That everybody who wants to come in at lunchtime, and work until the small hours force themselves around your schedule because you have a family?
Even jobs that are quite flexible are going to want some overlap time and, even if an atypical schedule allows for a few hours of overlap, the reality is that people will get tired of always having to schedule around your preferences.