What if the 8" Mark 71 was adopted?

The Iowas don't get reactivated.

I doubt that. They are very likely deactivated sooner, but realistically the reactivation was about bringing up the number of ships in service more than a serious belief (outside the Marine Corps) that fire support was important enough to justify the cost.

Assuming the Burke gets the 71 I'd think that the biggest effect is going to be that the Zumwalt's will look very different if they exist at all. My guess is designs will float around for something similar but that what will end up being built (alongside, as OTL, ever more Burkes) is a proper replacement for the Ticonderoga's, probably mounting dual 71s as a bit of a bone to the people calling for improved fire support.
 
About 5 km longer range than the 5"/54, but with a 25-40% lower RoF (depending on the version of the latter), plus well more than twice the weight (up to more than 3 times the weight in the case of the 5"/54 Mod 2), it will be of questionable utility at best
 
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