Just saw this Ran (Pesachim 26, dapei Harif). He discusses the opinions regarding the bracha on Hallel at the Seder itself.
1) Make a bracha, either at the meal or in shul, whatever comes first. Saying it in Shul seems to be a "Good Thing", but not obligatory (based on Meseches Soferim).
2) He quotes Rav Hai Gaon as not reuiring a bracha, because "This is not kerias Hallel, but a shirah", as we say in the Haggada Lefichach... "and thus we must praise etc."
(Ed. I assume he means that it doesn't need a bracha because the shira is part of the Haggada "experience", which itself, for some reason, doesn't get a bracha.)
This would then support either not saying it at all in shul, as we haven't said the Haggada, and certainly not saying a bracha.
That said, the continuation of the Ran seems to indicate a different reason for not saying a bracha at the Seder, which conforms better to Meseches Soferim, as well as a Yerushalmi he brings. He writes that since people who say a bracha in shul wouldn't say one at home, Chazal "made things equal" and removed the requirement for a bracha.
This approach clearly assumes that shul does get a bracha, (and Seder should but doesn't) but doesn't fit with Rav Hai's reasoning of shira.
The Tur, AFAIK, implies that since the bracha on Hallel at the seder is a dispute, it's good to say it in shul with a bracha, which fits with the Ran himself.
So, in summary, the original opinion of Rav Hai not to say a bracha at the seder would also account for not saying a bracha anywhere else. If the Chazon Ish was worried about that, that may be why ruled against saying a bracha. The reading of Hallel is then simply in deference to the Meseches Sofrim passage which implied that it's a "Good Thing" to say it in shul.