A submarine with nuclear missiles surfaces. It cannot reach its headquarters. There are "enemy" ships in the area that are heading towards it, including another submarine. So it can't just go back under the water safely. And even if it could, it can't communicate or launch while under water (it may actually be able to launch from a small distance under water but assume that it will be beyond that).
If the submarine does nothing and there is a nuclear war that already started, then the enemy ships will probably be able to destroy it. It is convinced that the choice is between launching its missiles now or not launching them at all if there is an active war. So your "long time" has gone down to mere minutes to make the decision.
In your proposed system, the submarine would almost have to allow itself to be destroyed in that situation. Because it's possible that this is not part of a nuclear war but just a series of bad events. But its missiles would be lost if it were a war.
So to launch a successful attack, the first thing that you would do is to send your navy to destroy all the submarines. You don't have to attack the enemy country itself at all. Just destroy the deployed submarines. The more that you destroy, the more resources you can concentrate on the remaining ones. So long as the submarines' country doesn't know that you are sinking them, you haven't shown them an act of war yet. They don't even know they are under attack. Once you destroy those at sea, use nukes or even conventional bombing runs to destroy the ones at harbor.
No mutual assured destruction (MAD). You just destroyed the enemy country without them getting a missile in the air. Why haven't countries done this? In the current system, there are still two more legs of the triad. Even if successful, you haven't eliminated the threat. And if not successful, you've triggered MAD.
One counteragent to this is to make the original scenario more paranoid. When the submarine faces the use 'em or lose 'em scenario, it uses its missiles. But now, if you can create that situation, you can start a nuclear war.
Who would want to start a nuclear war? Well, what if you are a relatively small terrorist organization in the middle east. You know that you can't defeat a nuclear power like the United States, Russia, or China. But what if you could start a war among them? The kafir would kill each other and stop meddling in your business. Some may tell you that radiation and nuclear winter will kill off people who aren't targeted by the bombs, like you. But you don't believe them. Just more kafir lies.
You compromise the Russian or Chinese intelligence agency and use it to gather information about the United States' protocols. All you really need is enough information to trigger them. You want the submarine to go underwater for a period where it looks like there might be problems. Give them the entire period under water to worry. Then when they are scheduled to resurface, cut their lines of communication. Create provocations that put ships they'll regard as enemies in their area.
The television show Last Resort had a similar scheme. It was foiled because the surfacing submarine wasn't worried enough. Their communications were partially subverted, but they chose not to believe them. But even there, it was a close thing. A captain who had a better relationship with the person subverting the communications might well have launched. Several of the officers thought that they should.
That of course was fiction. But it was intended as a realistic possibility.
The current nuclear triad means that we don't have to rely on any one agent. Even if an enemy destroyed all our submarines, we can still send bombers or fire ICBMs (Inter-Continental Ballistic Missiles). Attacks that work well against submarines may be useless against an ICBM.
With just the submarines, to match the current deterrent, the submarines would have to be more aggressive. Which gets us right back to the original problem of making a decision with insufficient data. Only we've moved that decision from the capital, which has as much data as possible, to a submarine that has been out of contact for days.
I also think that you overestimate the concern of a false launch. If there is one unexplained thing that might be a missile, you don't have to respond immediately or even before it lands. Even if it takes out one or even two launch bases, that leaves the rest of the land and air based arsenals. Beyond that, even if you lost the entire land and air based arsenals, you still have submarines.
If you scramble your bombers, they are in the air and can be called back. While in the air, they aren't that subject to attack via nuclear missile. You can delay the ICBM launch until the last moment. And you still have the submarines. So you have the option to not respond irreversibly.
With just submarines, you have less of a margin of error. Instead of watching out for a nuclear attack, the real danger is an attack on the submarines. They operate remotely and spend long periods out of contact. So losses aren't noticeable at first.