Player to DM: "I want to roll Initiative now, so I can Ready for Black Bart to draw."
DM to Player: "But the combat hasn't started yet?"
Player to DM: "But I'm sure it's going to.", as he rolls his dice.
DM to Player: "He senses the increased tension, and ... ", rolls dice, "his fingers hover near his gun."
Player to DM: "Ready action for him to go for the gun..."
Even if I disagree with the idea that you can't Ready for someone to come in a door, the objections are easily handled using normal mechanics.
The question is, do you dare to Refocus and then Ready?

Guarantees top billing in the Initiative order, in case both are Readied.
The real question is, do you always give a surprise round? I don't.
If each group knows the other is there, and knows a fight is brewing, we go straight to initiative. If the situation may or may not escalate to combat then a surprise round is possible.
Odd note: I ran an adventure that included sporting events. One was the 100 yard dash.
PC Barbarian thought he had an edge because of high base movement. And when the starter called, "Ready! Set! Go!", he Readied his action for "Go", to get that starting jump on the others.
He lost the race, of course. The more experienced runners went on Hold action instead. They start the race a heartbeat later, after the word "Go" is said, instead of the middle of the "G", but they get a full action, instead of the partial action the Ready lets you save.
His 40 foot move, on a full run (quad move) would be 160 feet. Their 30 foot move on a run (5x move with the Run feat) would be 150 feet. He should have won the race, but poor tactics cost him.
And, if you do the math, yes, good sprinters in D&D run the 100 yard dash in 12 seconds flat. World class sprinters (Barbarian base + Run feat) do it in 11.25 seconds. Don't you just love it when game rules give real world credible results?
