The Paladin would be reasonably effective as the balanced approach shifts 2/3rds of the weapons and defenses into other types. You are ensured that at least 2/3rds of your weapons, and 1/3 of your defense is effective against what your opponent has. In addition, the square root of the off-type defenses would apply to defense.
However, a Paladin would lose its effectiveness if pitted against another Paladin, as it would be facing off against a similar build so it wouldn't have a design advantage that the other guy doesn't have. You might have a tech advantage, but not an advantage balance wise.
Secondly, looking at the blueprint files, it seems that the Paladin is supposed to be fitted with more weapons and defenses early on than a different type of ship the same size, but it gets this by sacrificing engines and life support (till it gets enough room later to catch up). This means that it might be tougher early on, but it also means that it will likely have trouble getting anywhere. This means that if I knew that I was facing an opponent who was using Paladins, I might fly my Corvettes (medium hulled laser/shields ships) past the Paladins coming to my worlds and target my opponent's colonies and shipyards knowing that it would be difficult for them to turn around and catch me.
Thirdly, going specialized means getting more powerful weapons and defenses, something that a balance approach is not. Researching and using 3 different weapon types might mean that 2/3rds of your attack gets to bypass your opponents defenses, but if your opponent instead researches the next generation of weapons that doubles his attack with one weapon type, then it gets 2x the attack against your 1/3rd (plus the square roots of 2 off-type) defense. Furthermore, you can research techs that make your ship parts even better, which will widen this gap. Picking 3 price reduction or size reduction techs for 1 type of ship parts and using those parts many times means you benefit from those stats many times. You don't get this so much if you use a mix of 3 different weapons types, but only lasers has price reduction.
I think that what I'm trying to say is, you face trade offs. You could be good at something and exploit that advantage, but keep in mind that you will lose out on stuff and there are counters for what you do. Knowing what your limits are is half the battle.
I agree the biggest problem with a "generalist" approach is that it consumes a lot more research, which the other guys (or AI) are using to increase their tier. The fact that a pally against a pally is a draw isn't a problem, though, because the idea is not to get owned, not to dominate. And you make a great point about the load out. With all that defense and different weapons, a paladin build is going to suffer somewhere.
It has been opined elsewhere that a prime concern for ship building ought to be speed. A slow moving tank will have a role only in static defense for shipyards, etc., and can easily be bypassed by a nimbler opponent. I have seen it written that one's task in galciv is not to destroy the other guy's fleet anyway. It is to take away their colonies and keep moving. Back to weapons, evaluating ship vs ship only on the basis of offense vs defence isn't enough. Support ships with special things like jammers, fleet speed, tactical (thrusters) speed, etc. are critical components.