Earlier quoted context omitted.
Strategically crucial in a Pacific that had seen most everything the Japan side of Midway fall. If Midway had fallen, New Guinea, Coral Sea and Fiji were next in line, putting Australia and New Zealand at risk. What you call minimal gain would, had Yamamoto's plan come off, have put over 60% of the Pacific under Imperial Japanese control. US would have been fighting their way across the Pacific, island to island at a…
Granted, Yamamoto himself had no illusions re: a protracted struggle between Japanese industry, vs. American industry of the '30's/'40's era. Assuming no loss of political will, I suspect even in a worse case scenario where the US lost all its 3 carriers, it would still have eventually produced enough to win the war. Just maybe it would have taken several years longer...
One of the best visualizations I've come across of just how dominant the US industrial base was in the 1940s under full mobilization.