"should have opened" is correct and usable in written English.
It expresses a past regret or regretful suggestion. Example: "I should have opened the window before I left to let some fresh air in."
However, the Clarets started strongly and should have opened the scoring inside the opening 10 minutes when Austin got his head to a Ross Wallace corner only for Alan Navarro to clear off the line.
(Note to self: this is possibly the sentence I should have opened with. Yes, he showers, naked, within five minutes of the opening episode. Pope on a soap).
These examples should have opened the floodgates.
Her talent alone should have opened all doors.
After North's pass, East should have opened one no-trump, showing 15 to 17 points.
I can't wait to see you, you should have opened the yellow door.
The government should have opened a national investment bank to fund a huge housebuilding programme.
This is the play the revamped Everyman should have opened with.
The visitors should have opened the scoring in the seventh minute.
Variety's Andrew Barker criticises this strategy, arguing that it should have opened a week later.
Here, since West would assume that East had only five spades, especially when nonvulnerable, East should have opened three spades.
