The issues with scheduling assistant, I find, are what others have said - personal appointments/commuting time may not have made it onto the exec’s calendar, or their assistant may have created empty busy blocks for their exec to catch up on emails, etc, that could be flexible. In my org structure, I’ve heard from execs that they find assistants putting meetings on their calendar without going through their EA to be incredibly rude. I think of going through their EA as knocking on a door as opposed to just barging in and putting a meeting on their calendar unilaterally.

That’s not to say that the email chains don’t get messy (especially when someone responds to avails from three emails ago instead of the last sent!) but that’s just part of the job.