This might scale but not in the way you might think. Shell weight goes up with the CUBE of diameter.
A 5"/54 shell weighs 70 pounds
An 8"/50 shell weighs 335 pounds.
A 16"/50 shell weighs 2,200 pounds
Propulsive force required increases similarly.
There are a LOT of factors that go into getting a hit with a naval gun. Other than the obvious, there is the matter of the consistency of shell weight and propulsive energy.
The key item here, other than the increased range, is the guidance system built into the shell. A 5" gun can put out 16-20 rounds a minute. A 16" only 2 rounds. Then there is the accuracy to take into account. Currently, we get 80-90% hit rates with a 5" while 16" is only about 1-2%. Assuming you could get the accuracy of a 16" up to 30% you could get the accuracy of a 5" up to around 98-99%.
You don't need to sink the enemy to win. Given the construction of modern ships, I would much rather hit the target 5-6 times very fast and get a mission kill than maybe not hit them at all.
There is also the issue of the construction of the ship necessary to mount the larger gun calibers. Back in the early 80s we mounted the light weight 8" gun on the USS Hull as a test platform. It had previously had a 5" with no issues. The 8" shook the ship apart and drastically shortened the ship's service life to the point it had to be decommissioned. We can, and do slap a 5" on all kinds of ships with no issues.
Now consider scaling DOWN the shell size. The 76mm has a shell weight half that of the 5" (126mm) but a rate of fire that is four times greater. With the same hit rate, you can get twice the weight of shell on target at roughly the same range as the current 5".
Hope this helps. If you still have questions, just ask.
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