Iraq's Military and the US Withdrawal: a paradox?

Until 2003, Iraq had a military that was very much in control of that
country's security. Then nearly a third of a million troops came in,
displacing but by no means killing Iraq's soldiers, most of whom,
along with the police, remained.

Since then, the invading nations have insisted they stay on the
grounds that "Iraq's military is not yet able to control the country."

Duh?

A hugely powerful Iraqi military machine, further funded and
munitioned by the USA, and lacking only a dozen or so of Saddam's
political-military generals, but the US says it "is not able to
control the country".  What sense does that make?

Given Saddam Hussein's deep rooted hatred of Al-qaida, maybe we should
have left well alone in a nation whose military WAS very clearly in
control of the country.

Forty years ago, Britain's Labour prime minister Harold Wilson, was
asked whether his government would "recognize" the fascistic coup
d'etat by the Greek colonels' junta.  He replied that recognition of
another government was based not on like or dislike, but on WHETHER
THAT GOVERNMENT WAS IN CONTROL OF THAT COUNTRY.