The big trouble here is we are not talking real world information. Yes in reality some naval guns were far superior to what they should have been on paper, shell, powder technology and so on also created many different results.
But in the game we are given some numbers based on what modules we fit on the ship:-
A 16" Mk3 Gun, regardless of nation, using High TNT Propellant has the following numbers (currently):-
Super Heavy Shell - 1775Kg, MV 699 m/s, 31.3Km Range
Heavy Shell- 1592Kg, MV 719m/s, 30.6Km Range
Standard Shell - 1224Kg, MV 777m/s, 29.2Km Range
Light Shell 857Kg, MV 874m/s, 27.8Km Range
We don't know what angle of elevation the guns can reach - the game does not tell us - but given that a shell fired with air resistance reaches its maximum range at somewhere around 38 degrees of elevation (and many Battleships had about 35 degrees in reality presumably for this very reason - no need for more elevation, the shell won't go any further - unless you plan for AA use). The trouble is that given these numbers its clear to see that the Light shell leaves the gun at just short of 200m/s faster than the superheavy, over a 25% increase in starting velocity. When things are equal, (and I am going to assume for the sake of simplicity that they are here - as in the Light and the Superheavy shell have the same cross section - both being 16" and the same drag coefficient - both being the same shape shell, and both leave the barrel at exactly the same speed and at the same elevation), then the heavier/more dense projectile would go further than the lighter/less dense one, air resistance having less of a slowing effect on the heavier shell.
BUT and this is the problem - Its NOT equal, the lighter shell starts at 25% greater speeds, it will reach a greater range, I can't say exactly how much, we are not given enough information to work out even a close approximation, but it would go further, and due to the higher starting speed would cover shorter distances, before it had been slowed by air resistance, more rapidly than the heavier shell. Less time in the air, means less time for the target to move, means errors in calculations, gun dispersion, wobble in shells, air resistance, pressure and so on have less time to affect the shell which makes it MORE accurate. It just does a lot less when it arrives.
If the game designers want Super Heavy shells to have the longest range then all they need to do is equalize the muzzle velocities across the board, or simply delete the muzzle velocity data.
Further to this but in the same general area - 8 inch and greater guns could generally fire just as far as their bigger cousins due to firing a lighter shell, faster, and with a better elevation. (Currently in game lighter gun = less range e.g 10" Mk5 Superheavy range of 22.2km with 875m/s initial velocity, light is only 19km range with 1093m/s velocity).
I will say that yes gun wear, and the associated accuracy and cost ramifications, with higher velocity shells is a HUGE reason why not many nations went down that route. HMS Nelson tried high velocity 16" and changed back to lower for several reasons but rapid barrel wear was one of them.