Because 12" isn't enough to really scare enemy battleships yet it denies tonnage to the battle line. It's great to have as a scout to punch through the enemy's screen, but not at the cost of hobbling your own battle line.
Now, I agree that 16" is too much - I only mentioned it because I remembered that there was a triple 16" turret available and the demands of tonnage and sufficient guns for spotting favours two triple turrets. These things are using battleship tonnage and must be capable of harming enemy battleships - and 12" just doesn't cut it.
The problem with that line of thought is that as soon as you have a ship that can threaten a Battleship it is meant to be used against a battleship. Any ship built to 23000 tons that is meant to fight a Battleship is going to be limited in and not really able to match it. The 2 forward turret layout is good for preserving weight in armour so you can have a thicker belt say, thing is that is very vulnerable to both turrets being taken out by a single enemy salvo or even a single hit. then your ship is useless until at least one turret can be brought back online.
The big advantage of a fast 12" or even 13.5" ship is scouting for the battlefleet. That role is still of vital importance right now, yes over the Next decade the aircraft carrier will take on that role but as things stand that's the role of a battlecruiser. I'm advocating for the best way I see for the royal navy to spend the tonnage in a way that suits their doctrine and thinking within the confines of this story and OTL thinking from this time period that is likely to be similar here. My actual advice would be rebuild the battlecruisers you have to carry out the raiding and scouting role and spend all your tonnage on Battleships, ignore the light battleship its a dead end. Actually thats a lie, my actual advice to this alt RN would be to use the 23000 ton limit to build large aircraft carriers backed up by large, 40000 - 42000 ton fast Battleships but that wont happen. At least the 12" ships I suggested will be useful support to a carrier with all the AA I put on the second design at least.