Sir Brennen
Legend
Once when I was running a game of 13th Age (which uses the standard d20 initiative system a la 3e/4e/5e) the party was exploring a tomb with the paladin in the lead. When he entered a room with a bunch of skeletons in it, I called for initiative rolls. The result was that the paladin had to go last despite being in the front and being fully ready for combat. This didn't make any sense in the fiction and the only justification would be to say he stumbled for some weird reason or was uncharacteristically passive, either of which would go against the type of heroic and cinematic gaming I like. I saw this as a huge system fail, so much so I immediately started looking for alternative methods.
I think establishing PC initiative outside of combat, like [MENTION=6774924]secondhander[/MENTION] suggests, is a great idea for situations like this. When the party approaches a door, go through the existing initiative order and see what everyone is doing. PCs who have a higher init than the paladin can act, but they are doing so *before* the door opens. The cleric casts a guidance cantrip on the paladin, the rogue hides (bonus action) then Readies (Action) to fire his shortbow at the first creature he sees when the paladin opens the door (using the rogue's Reaction). Then on his init, the paladin throws open the door, sees the skeletons, and charges in to attack. Sure the rogue gets his arrow off first, but it now makes sense in the narrative (he was ready!), but he's not running into melee ahead of the paladin. (He could run in, if that was his Readied action, but he couldn't also attack).
In fact, I may have to incorporate this as a house rule into my current game. I.e., have players roll a "non-combat" initiative at the start of the session. Ask them what they are doing in any given scenario (hex crawling in the wilderness, searching a room, having dinner with the duke) in init order. When someone does something to start a fight, just continue from there, using the existing order for combat initiative. Then roll to "reset" initiative *after* combat, and perhaps after every long or short rest. Then there's no "you attack someone? Roll initiative!" where the character who literally initiated combat goes last. Combat is just something that happened to begin in the middle of the initiative order.