Hiya!
I agree with your disagree, but disagree with your thinking.

Let me 'splain....no, t'would take too long. Let me sum up...
It seems that after 5 pages of thoughts and post it is obvious to me that the "Ready", "Surprise" and "Initiative" rules don't fit with this scenario. Each have parts that fit...but not comfortably. Luckily for us 5e has a rule to cover that. It's called DM adjudication.
If a situation doesn't fit a rule, or you can't find a rule to cover some situation...
ignore all the f'in rules and just make a ruling! Seriously. I don't know how many time I have said this...when in doubt,
make it up.
In the situations above here's how I would play it out:
Players: We get ready to shoot. Bill opens the door and we let fly the arrows and slings at the enemies beyond!
DM: Ok. Bill flings open the door and you see bandits with crossbows pointing at you guys. Roll to hit [I also roll to hit for the bandits against those who can be seen, randomly determining which bandit shoots at which PC].
---hits are noted, damage is rolled---
DM: Ok, two bandits are down, three remain that you can see. What does everyone want to do? Then roll Initiative.
That's how it would play out in my game. The whole "surprise, initiative, ready, whatever" rules don't fit well enough to be used...so I don't use it. Oh, and, IMNSHO, that's the way the game is supposed to be played. If your game just came to a grinding halt for more than a minute if/when this situation showed up, you're doing it wrong. Make a ruling that is reasonable and fair and keep the game moving. Nobody will care about rules minutia or other rule-lawyering shenanigans if they are all having fun trying to overcome the bandits, pressing onward deeper into the dungeon, and keep on trying to recover the Magic Foozle from the Undead Bandit Lord of the Haunted Maze.
^_^
Paul L. Ming