Admirals have commanded fleets from light cruisers. If a light cruiser has the room for it surely a heavy cruiser, battlecruiser, or battleship can find the room?
Some light cruiser were constructed with Flag Quarters, many were not.
The simple fact is that the CB were POORLY thought out. They lacked basic defensive features that would be expected on a 32K ton design, including torpedo bulges, and armor capable of handling even late war 8" AP rounds.
All the ear-rings and lipstick ever made won't make a pig anything but a pig.
The Des Moines class were intended to use super heavy 8" shells, which were a limited procurement item (although they were also used on older cruisers).
The Soviets were also considering more powerful
Stalingrad class battlecruisers, and the
Alaska and
Iowa class would have been the only ships with the speed, firepower, and armor to match them.
Exactly how many 12" Mark 18 and Common Mark 19 shells for the new 12/50 Mark 8 gun do you suppose were procured? In addition to being a new gun, it used a new shell in order to achieve its exceptional performance (for caliber) The Navy only made a TOTAL of 30 12"/50 Mark 8 barrels, unlike the literal hundreds of 8" guns produced.
If the U.S. wanted to fight a Soviet BC, the answer wasn't to go out with a peer (bad stuff can happen when you fight an equal, especially when the CB can't handle 12" gunfire,
HMS Queen Mary ring any bells?), it was to go out with a
Iowa. Finish the last two BB-61 class ships; if the need is that great, build a couple more (or, much more economically, keep the BB-55 & BB-57 classes in service). The Soviets want to fight on a day when it is impossible to fly, let them come in and fight the heavies while the carriers do exactly what they should do, fall back with their DD screen and let the big dogs fight.