First of all, we're not talking about what occurs while combat is taking place. We're talking about what occurs at the beginning of combat, when acting against an enemy "NOW" may be impossible or impolitic.
In which case, if we're not talking about when combat is taking place, there isn't a real need for initiative. Initiative rolls are a
random determination of who goes first. Adjustments may apply but it's still random. When talking about about how you DO initiate combat without then suddenly being subject to random determination, just be the first one to state you ARE acting. That gets you to top of the order in my games. When commencement of an action is conditional upon someone else's action, then usual rules regarding Readying actions would apply, but SOMEONE begins the chain reaction, and as I said, first to say they act, acts first. When the situation is one of general, simultaneous commencement of hostilities, then random rolls are appropriate.
Secondly, your attempt to add nuance just adds fiddliness to the adjudication, takes up even more time, and generally adds an adversarial element to the exchange between player and DM.
Never has for me. It was a
solution to the problem of abuse of Readying (at least in pre-5E games where Readying was a thing).
"I move down the hallway and ready an attack if there is a hostile creature." "Okay, do you ready to attack with a sword or your bow? What action are you readying against? How far do you move? Etc." "Fine: I move 30 feet down the hallway and ready my bow to shoot the first hostile creature who appears within range of me." Do you want your players doing that every 30 feet of every hall?
Nope. And they don't want that either. Besides which, if you're moving down the hall you're not readying, you're moving down the hall. If they want to state they are moving down the hall and are expecting to see opponents to shoot, and have reason to expect that to happen rather than just taking a guess that it might happen, then I have no problem
giving them initiative, rather than rolling for it. In a specific circumstance where they have reason to expect to suddenly see opponents to shoot, and state that they proceed on that expectation, they're doing things properly and don't need to Ready anything. If they have no reason to expect to see opponents to shoot as they move down the hall, but want to try to READY to shoot just in case they do, that flat out won't work.
The alternative I humbly propose is to assume in good faith that competent adventurers are behaving this way, offload the burden of determining who draws first onto the game system that was designed for precisely this purpose, and get on with exploring the dungeon.
I do assume in good faith that competent adventurers (and players) are at all times attempting to be aware, prepared, and willing to act
instantaneously as necessary. They attempt it always by MY default assumption as DM. But no amount of tedious attempts to become impossible to catch off guard, or to always act first by constant, never-ending Readying is going to work, effectively because Readying doesn't work that way, nor for that purpose, and I think I'd be a poorer DM if I let it be.
But as far as the game is largely concerned, initiative is always random. That's a problem. It prompts questions as we see in the OP - how DO you catch someone off guard without initiative determination then getting in the way. I'm saying that while most occasions where initiative gets involved it IS randomly determined, there are also many situations where ASSIGNING initiative is more appropriate. Like when everyone is in a standoff and someone finally says, "Enough of this. I ATTACK," or, "My PC runs and dives for cover." That character gets top of the initiative order. Not advantage on the roll or additional bonuses. He goes first because that is appropriate in the situation, and random determination of his order in initiative would not be. That is not BTB rules, of course. It's
my way of handling the issue, which is what I believe was requested.