If you have more specialized ships then having more CP is really worth it. For example i frequently have a very dedicated pd ship that i have go where ever the most fighters are. I like to make ships that are high Explosive/Kinetic mirrors of each other and always have them pair up for assignments. The assignment system gets a little finicky so it sometimes requires fiddling. If i have an EMP ship like shade or omen i manually have it flank the big mastery ships like dominator or onslaught.
As was mentioned they're invaluable for fighter fleets. If you don't clump on targets then your fighters will be torn to ribbons piece meal. It's also handy to move your carriers to just behind the front lines. Especially now that the pilums range is effectively 7K instead of 10K SU.
You can build a big fleet of balanced ships that are all able to handle themselves in most situations, but sometimes that's not good enough. Like when you start going after combat 10 bounties. In situations like that i really wish i could apply 2 or more commands to the same ship. Like have bunches of long ranged ships harry and then have all my bombers strike them when close to overload but not have my previously harrying ships derp around and fight other things.
You can build a big fleet of ships that can handle any and all comers with minimal CP needs, but it involves exclusively t1 and t2 ships with ideal weapons, meaning that losing even one frigate in that fleet is a pain to recoup. I do it with a Paragon, 2 Dooms, and some tempests, shades, and afflictors (I find those to all have a very high survival rate).
Anyway, the way the AI works a lot of what you suggested either doesn't work or requires tricky workarounds like grouping/ungrouping to disengage. For instance, having those paired shield/armor killers is pointless compared to putting shield/armor weapons (or just energy) on the same ship. Reason being they are both going to fire at once at whatever target they feel like regardless of what you tell them to do, so the net result is the same. Specializing is more worthwhile when you have a strategy to go with it, put shield killing weapons and then armor killing missiles or emp, or send armor killers against front/no shield targets while you personally keep them occupied, but none of that actually requires CP to be effective.
On an unrelated note, not a fan of Pilums. Putting those on a ship is like saying "this ship not participating in battle". They are far less effective 90% of the time than simply having another frigate in the fray.