This happened.

The only likely reason why Variant Phalanx’s ships ‘refused’ to use Cruiser Lasers and Plasma weapons is simply that the weapons were out of range. Multiple Warhead Missiles have a considerable range advantage over cruiser plasma and especially Cruiser Lasers (in fact, Cruiser Lasers and Multiple Warhead Missiles cannot fire on the same target at any point, as the minimum range of an MWM exceeds the maximum range of a Cruiser Laser). This does not make either the cruiser laser or cruiser plasma bad, but it does mean that it’s not necessarily a good idea to mount both on the same ship; cruiser lasers are only an appropriate weapon on a missile cruiser intended to be able to handle rushes, as the laser will never come into play if the engagement is fought at standard missile ranges, and plasma doesn’t really do anything that missiles don’t.

Missile spams and plasma spams are roughly equally effective long-range fleets, with missiles being longer-ranged and plasma being a bit harder to counter with defenses (due to immunity to PD and scramblers, as well as to slightly higher armor penetration); as plasma range is more similar to cruiser beam range and generally has somewhat higher armor penetration than missiles, it’s also a bit better against armor-heavy fleets (missiles are also somewhat less appropriate as a weapon to pair with beams because sacrificing missile density to gain the beams can be crippling if fighting an opponent with decent PD or especially scramblers). Cruiser lasers are an entirely different weapon, best suited for and very effective on fast cruiser designs but also useful as a close-range weapon for long-range warships in case something survives the long-range bombardment long enough to engage. Note that a long-range warship that sacrifices a missile or plasma for a cruiser laser is probably going to lose against a pure-long range warship (the laser will never come into play, so you’ll have sacrificed power at range for no gain in such a scenario) in a similar-numbers scenario.