Illums can be good, in close range, the LRM missles spin around your ship a few times before finally getting hit, while illums can get close and the three guns (front and one on each side) will definetly hit. So bring your illums in close range to the LRMs. try something like that, make your illums fly over the LRMs and the back again, they will spend all there time turning around while your side guns take them out.
Illuminators only deal 75% damage to other LRMs, they are less cost efficient, and all their beams will not hit most of the time, meaning they'll operate at 33% or 66% efficiency most of the time.
Scouts
Doesn't work. Scouts are only statistically superior to LRMs because they have more health for the same cost, they both have the same DPS for cost, but LRMs can kill anything while scouts can only kill LRMs.
The LRMs will fly past your scouts, kill your Cap Ships, Research Centers, Light Frigates, etc. The scouts will manage to wipe out the LRMs as the LRM wail on your econ.
A few minute later you get attacked by a wave of Light Frigates, Carriers and Flaks, and your fleet cap is still filled with scouts. You lost the game.
Flak Frigates
They are like the scouts, but with an even more magnified problem. Lower DPS but much higher health than LRM. The LRMs will ignore the flaks and wail on your Caps & Econ. The next wave will be Cobalts. You lost the game.
Carrier Cruisers
Carrier Cruisers with all fighters are only 15% more efficient at killing LRMs than LRMs are efficient at killing Carrier Cruisers. Carrier Cruisers are slow to build, and once built they need to build their fighters (2.5 minutes for Advent).