The CR has a lower credit cost, but has a construction cost 3 times higher. I can build 3 BC for every CR.
The BC should be compared to the standard+armor section, not the war+strafe. Even with that they mount more large guns. Not having the same alpha strike capabilities does not make it worse at doing damage, it changes its role from a line ship( a ship you keep in tight groups to overwhelm targets in single volleys) to a harrier (strike and harry, used to corral ships into your firing ranges and harass) The BC is faster at top speed, better at maneuvering and accelerates faster to boot.
The DN doesn't lose firepower from the BC's. They are part of the DN, a part that can be independently replaced and swapped out. I can use the same carrier for 100 turns while the BCs weapons keep getting better.
I can bring the same amount of CR's and DN's into battle whether they are carriers or not. The carrier DNs give me extra ships in exchange for reduced firepower on the DN itself, but enhanced firepower when you consider that I now have 3 more cruiser class ships. So thats not really a minus, its a trade off.
please explain your example in more detail.
Edit: to be specific
Because Cruisers cost less, do more damage, have jump-drive.
where the BC that is supposed to be heavily armed cruiser: less effective in doing damage ( even if you are flying around, broadsiding, ), cost more money, require a dreadnought to operate ( because of that Dreadnought lose firepower)
Here you gave your opinions but did not back them with information. I can't delve your basis for these statement so all I can do is offer my opinion and the reasons I have it.