Here's one way to play it:
Let's say two beings (A1 and A2) come around a corner and find themselves face to face with a couple potentially hostile beings (B1 and B2). I'm purposefully not designating who is a charcter and who isn't as I believe it makes no difference.
Determine surprise:
Outcome 1 - Everyone surprised. Nothing happens for a brief moment while everyone stares. Surprise ends. Go to outcome 2.
Outcome 2 - Nobody is surprised. If anyone wants to attack, roll initiative, otherwise roleplay (Combat may begin later because someone is insulted, etc.).
Outcome 3 - Some of each side surprised. A1, B1 surprised, A2, B2 not. If anyone (even surprised beings) wants to attack, roll initiative and combat begins with surpise still in effect, otherwise roleplay (Combat may begin later because someone is insulted, etc.).
Outcome 4 - All of one side surprised. A1, A2 surprised, B1, B2 not. If anyone (even surprised beings) wants to attack, roll initiative and combat begins with surpise still in effect, otherwise roleplay (Combat may begin later because someone is insulted, etc.).
Parleying or fleeing are done in initiative order if in combat, otherwise as player's decide.
We still roll initiative if only the surprised party wants to attack because if the parties are close enough and the unsurprised one moves or flees, the surprised ones may be granted an attack of opportunity as a reaction, depending on initiative order.
I'm actually not opposed to the surprise rules as they are written, especially as they pertain to a scenario where two groups unexpectedly bump into each other. I think they work in most cases.
My contention is with when I have to call for initiative to start combat in certain instances like the one I outlined above. Personally, I'd just let that assassin take the shot with surprise.
The transition from "combat" to "out of combat" can be nebulous, IMO, and certain scenarios just don't fit neatly into D&D's system. Even when they do fit into the system, they can lead to some odd results if you run them strictly by the book. Take a look at the scenario below...
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Andrew the assassin, Biff the battle master, and Cory the (war) cleric are hiding out in the third story of an abandoned building in a large town. The setting sun can be seen through an open window, but there is still some hustle and bustle below in the streets.
Andrew spots the telltale markings of a town guard a few hundred yards down the road. The armor, the cloak, the standard issue halberd... even from this distance and at this time of day, he can spot one of the local authority. He recalls being thrown in prison last year in this same town for pickpocketing. Being a guy that holds a grudge against the establishment, Andrew decides that he's going to put his Sharpshooting assassin skills to use and put in arrow of the back of the guard.
Andrew draws his longbow. The group's earlier stealth check far exceeds the guards passive Perception score. Andrew's lips twitch with a wicked grin as he prepares to fire...
<CUE INITIATIVE>
- Andrew: 12
- Biff: 19
- Cory: 16
- Guard: 6
<ROUND 1>
Biff acts first but simply watches Andrew in anticipation. He, too, had a run in with the law here, so he has no qualms with a little revenge.
...but Cory, who acts next, decides that he isn't comfortable with this cold blooded assault! Cory casts
Hold Person on Andrew, and Andrew fails his save.
Andrew stands as still as a statue, incapacitated by the spell. He rolls a saving throw, but fails again.
The unwitting guard continues to stroll down the road away from his would be assailants. He's enjoying the sunset as his watch is coming to an end. Also, he's apparently no longer surprised, but he's not sure what that means.
<ROUND 2>
Biff is having none of Cory's sudden moment of good conscience. He punches Cory dead in the face. While it doesn't do much damage, the blow does break Cory's concentration on the spell.
Cory madly lunges at Biff, forgetting about the guard, and grapples him.
Andrew snorts derisively as he realizes he's free of the spell, and then takes his shot at the guard... a hit! But wait, no 'Assassinate' damage for Andrew because the guard has already taken his turn in the initiative order! Sorry, Andrew, try to be quicker next time, or bring some friends with looser morals!
The guard abruptly stumbles forward as an arrow suddenly strikes him in the back. The shot nearly killed him, yet as he grimaces from the pain, he can't shake this strange feeling that he was incredibly fortunate... if he can just make it out of the streets before the unseen assailant(s) can loose another arrow.