I could really see that. But rather than a warship bristling with every weapon imaginable, I could see it having a few weapons arrays that are decided on because they are the best weapons of their type, or combinations of technologies. (beam weapons would be, say, an uber-powerful version of the All Good Things Enterprise phaser, or a heavy Cardassian disruptor. The ship would be armed with a couple of transphasic torpedo launchers, say) [rather than 50 pulse phaser emitters, 8 heavy disruptors, 24 ion torpedo launchers, etc.
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Maybe each power would contribute their best technologies to the ship, like you said. Federation sensors, science labs, propulsion, a Romulan cloaking device and maybe weapons, Klingon armour and maybe weapons, etc., etc.
"With the first link, the chain is forged. The first speech censored, the first thought forbidden, the first freedom denied, chains us all irrevocably."
Jean-Luc Picard, quoting judge Aaron Satie