The second approach is the one used by the Zumwalts. Lots of stealth, making you a difficult target to acquire, and hopefully allowing you to "hit them before they hit you." Large guns require a large hull. Hiding a large hull is not conducive to lowering the costs of stealth. Those two goals work in opposition to each other. Reducing gun size then requires what was intended for Zumwalt...increasing range, and number of rounds per minute, to dump many smaller rounds very precisely on a target, to both destroy it with the smaller rounds and reduce collateral damage.
The navy found out repeatedly that small guns were largely ineffective in the shore bombardment role against dug in targets during WWII. The Zumwalts were a waste from the time they hit the drawing board.
Just try chopping down a 3-foot diameter tree with 5.56mm. With 7.62mm you can do it with ease.
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