Thinking about this a bit more...
I wish everyone would.
In thread of this type it's extremely important to separate what
they knew then with what
we know now. People always fail to do that, often unconsciously.
In this thread in particular, it's also important to separate what
they knew in April when the task force was being put together from what
they knew in late May when the task force had suffered losses at the hands of the Argentine air force.
Let's look at the possibility of including the Canadian AORs and destroyers from solely from a what they knew in April perspective. For this exercise, we'll assume that the ships are simply the UK's for the asking.
Logistics - The AORs will undoubtedly improve the task force's supply picture and defending the AORs, as was done in the OTL with most of the "fleet train", is only a matter of keeping those vessels beyond the reach of the Argentine air force. Remember, the
Atlantic Conveyor was only hit because she needed to approach the islands to operate/fly off the helos she was carrying.
Asking for the AORs and the destroyers doesn't improve the supply situation at all because the destroyers add to the task force's supply requirements. In fact, the destroyers are going to need items like munitions and repair parts that Britain doesn't have meaning Britain is going to be forced to get even more of the OTL "back channel" help from various sources.
The question now is whether what the destroyers bring to task force is worth the effort of supplying them.
AAW - The abilities of the Argentine air force caught the RN very much by surprise. There's that well know quote by a RN officer about how, because Argentina produces great F1 drivers, we should have know they'd produce great fighter pilots too.
The RN believe the various SAMs, guns, and countermeasures available to it would handle whatever aircraft and munitions Argentina could throw at the task force. An example of the strength of that belief
in April was that the
Atlantic Conveyor was not fitted with chaff dispensers thanks to some minor legal concerns. Fitting the dispensers would have been a simple matter of welding, but worries over a few words in a contract scotched the idea because the belief for the need for those dispensers in
April wasn't as great as the belief for the need for those dispensers in
late May when the burned out hulk of the vessel had to be sunk by the RN.
Apart from countermeasures, the RN's other AAW weapons and how they were used proved lacking too. The guns did provide a nuisance for the Argentine air force at San Carlos, but accounted for little. The various SAMs provided little more than a nuisance too. In the end, the tempo of Argentine air attacks was constrained almost solely by the amount of munitions available to Argentina and not by British air defense.
It's clear that, because they carried the same weapons, the Canadian destroyers wouldn't have helped much with AAW but the RN wouldn't know that in
April. So, the question returns to whether bringing the destroyers along is worth the increased supply demands their presence creates. I'd say no because the RN thought it already had enough of an AAW capability and the Canadian ships would provide nothing unique or special, merely more of the same.
ASW - This topic is far more murky. Neither government said much at the time regarding the activities of their submarines and both governments have admitted little in the nearly three decades since.
I feel the claims about the Argentine SSK must be taken with a grain of salt. The stories about her lining up for shots on British warships only to be foiled time after time by weapon malfunctions is too good to be true. The fact that the story only came to light more than ten years after the war, despite the fact that the junta would have jumped on any success story no matter how marginal and despite the fact that the members of her crew would have undoubtedly spoke up sooner, make these claims rather suspect.
Regardless of what the actual story is, ASW falls into the same general category AAW does. The RN felt they had enough and the inclusion of the Canadian destroyers ASW capabilities would depend whether the increase in ASW assets was worth the increase in logistical demands. As with AAW, the
Iroquois didn't bring anything unique or special to the ASW table, so, again, I'd say in
April the logistics question trumps all.
Shore Bombardment - The RN performed relatively little of this, apart from San Carlos, RN warships would perform fire missions at night and withdraw from the islands during day light. The need for shore bombardment was even less than that for more AAW/ASW capabilities, so, again, logistics wins in the end.
Summing up, logistics is the first and last argument. A decision to bring along the Canadian destroyers in
April would hinge on the RN's belief in
April that it had the AAW/ASW situation pretty much covered and that the logistic demands of the additional destroyers wouldn't be worth their contribution. The Canadian ships didn't provide any better or different AAW/ASW options and abilities either, so including them wouldn't provide the RN with something it didn't already have.
The only plausible way I can see for the
Iroquois-class to steam south with the RN task force is for the Canadian government to insist that, if Canadian AORs are used, Canadian warships must escort them.
And that might just be why Britain didn't ask for the AORs in the first place.