The way I was doing initiative prior to Mearls Sage Ruling was the following:
1. First hostile action. I don't roll initiative for non-combat situations unless I need to know the order of actions. Otherwise I let things occur in an organic fashion letting each player act when it is seems natural for them to do so.
2. I ran a surprise round when the first hostile action was taken. Everyone rolled initiative, so I knew when saves or abilities worked. Anyone surprised could essentially take no actions which I assumed meant they did not take a turn, though they did have a turn. I made a distinction between taking a turn requiring they take some kind of action on their turn and having a turn where they had to make a roll that wasn't an action on their turn such as a save at the start or end. I thought the game made this distinction, but I guess it does not make a distinction between "taking a turn" and "having a turn." I wish it did as it makes more narrative sense in my opinion.
3. Once past the surprise round, initiative proceeded as normal.
The surprise round made sense mechanically because it allowed you to adjudicate saves or abilities occurring on a turn, while at the same time allowing for the narrative idea that the target doesn't know that an enemy that hasn't acted is present. It was a mechanical method of denying a turn based on lack of awareness, while still adjudicating all mechanics based on a turn that don't require awareness. With Mearls ruling that narrative idea has been removed and I'm supposed to operate under the assumption that the target always has some awareness an enemy is present, which I find absurd. It devalues Stealth and Perception and overvalues initiative. You could have a 5 Perception and a +10 initiative and still act faster than someone with a +17 stealth. That is absurd to me. I do not know why Mearls feels this is how it should be. My only hope is Crawford sees this a different way at some point in the future.