It's an interesting idea at first but upon some brief thought, contrary to what you say, it seems incredibly strong as it is:
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harder to scout - compared to a regular anti-nuke, which only requires any unit with vision to see it once for you see the building, you need a unit with water vision (which only a few have) over the sub and you need to be watching right as your unit has the sub in its water vision, as it won't leave the unit/strategic icon behind since it's a unit, not a building.
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mobile - compared to the regular anti-nuke which is fixed in its location, the player launching the nuke cannot determine what the effective range of the anti-nuke is with this anti-nuke sub because it can move to cover multiple locations: the theoretical coverage is the radius of the anti-nuke extending beyond the entire body of water.
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versatile - it's literally a nuke + anti-nuke combined in one as per your suggestion, if you make one of these subs and your opponent has a nuke, your opponent has to react with an anti-nuke of his own unless he wants to risk getting nuked while you can just make an anti-nuke with the sub and be up 11k mass for free...
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probably going to be harder to snipe than the regular anti-nuke because you either need to use torp bombers, which are just a lot worse than strats, or groundfire strats, which likely can be dodged and is easily countered by the presence of a few sams/hover flak/asf because you need to keep t3 air scouts over the sub in order to ground fire a moving target that's dodging accurately.
If anything, it should cost far, far, far more, not less, than a regular anti nuke for it to even be remotely balanced. In general, I've been surprised by a nuke from a nuke sub far more frequently than from a stationary nuke, and I expect that will be the case with this. I am firmly against adding anti-nukes to existing subs for the above reasons.