This is not so strategically illogical if you think of a cabal of rogues in any of those states, rather than thinking in terms of official sponsorship.
As for the idea that the letters were sent to frame Iraq: How do the anthrax letters frame Iraq anyway? They don't mention Iraq, they don't allude to Iraq. In context, they would seem to frame al-Qaeda if anybody. The text:
"Death to America. Death to Israel. Allah is Great."
makes me think of Iran, if anybody.
So how could the perpetrators have known that Iraq would be blamed? And, if they had wanted to get Iraq blamed, wouldn't they have pointed more directly to Iraq in some way?
Another point: It is said that Iraq used the Vollum strain in its anthrax production. If one wanted to frame Iraq, that strain would have been a better choice than Ames.
And how did any of these foreign candidates get virulent Ames anyway? Whether it was a domestic job or a foreign job, you can't get away from some U.S. connection.
Think about it. The idea here is that the anthrax conspirators were a completely separate group to the 9/11 conspirators, but that they wanted their work to be perceived as of a piece with 9/11. In other words, after a shadowy terrorist group had just killed thousands of people very publicly and gruesomely, the anthrax conspirators immediately set out to create the impression that the same group also had access to a weapon of mass destruction. It's an action which seems more likely to flat out deter war against the terrorists, than to channel the war in a particular direction, which is the intent usually ascribed by the 'insider' theories.
How do the anthrax letters frame Iraq anyway? They don't mention Iraq, they don't allude to Iraq.
Just three years before, the USA had intensively bombed Iraqi WMD facilities, and had adopted an official policy of regime change in Iraq, out of fear that weapons like anthrax might be passed to terrorists. The Secretary of Defense went on TV and specifically said that a small bag of anthrax could kill half of Washington DC. The Iraqi biological weapons program was the greatest source of concern for UNSCOM. Iraq admitted that it had managed to weaponize anthrax, albeit in liquid form.
So it's the mere presence of weaponized anthrax in the letters which was guaranteed to make people think of Iraq. As you say, the text in the letters ("DEATH TO AMERICA") is more reminiscent of Iranian sloganeering.
The question of Iran, Iraq, and al Qaeda sponsorship reminds me of one of those logic puzzles, where you have (say) two giants at a fork in the road, one of whom always lies and one of whom always tells the truth, and you have to figure out which road leads to your destination by asking just one question.