"should have requested" is a correct and commonly used phrase in written English.
It is used to express something that someone should have asked for or requested in the past. Example: "I should have requested a raise during my performance review last month."
Perhaps for my own sake I should have requested it.
That is what Mrs May should have requested.
Mr. Kuby said the district attorney's office should have requested a court order to obtain blood from Ms. Jordan.
Critics complain that the Obama administration should have requested more than $1.8 billion for FEMA in 2012, but the White House says billions more will be available.
Rupert Murdoch should have requested her resignation on the day that he discovered she was editor of the News of the World when Milly Dowler's phone was hacked.
The court said that new DNA tests would not prove his innocence, and that he should have requested the testing at his original trial.
So as a result, we elected not to carry Mr. Rushdie, should he have requested to fly on Air Canada," Ms. Cook said.
Morris went further and said that we should be going more aggressively against the protesters, that it was a mistake to have urged the military to stand aside and that we should not have requested pro-Mubarak supporters to refrain from violence.
"The planned execution of Marshall Lee Gore had already been stayed twice by the courts, and we absolutely should not have requested that the date of the execution be moved".
"Obama should not have requested more troops because doing so intensifies opposition to the war in the US and Europe and accelerates the pace of withdrawal demanded by political pressures at home.
The only facts you should accept are ones you have requested and paid for, i.e., an education.
