The GTVA has multiple vital rear-area targets in Sol that must be defended, including but not limited to the node. Those become open to attack. You could counter this by 'strategic sprinting', which is not something we dismissed offhand but something we think about. Unfortunately said sprints tend to turn into cluster****s.
The GTVA is a conquering army.
Either you're suggesting that they have been stupid enough not to centralize their logistics at the node (this is the subspace age, centralize wherever possible, dispersal merely puts more of your ships at risk), or that they in fact have conquered territory that they now feel compelled to defend, which both contradicts your statements below and also is unnecessary. You have already ruled out amphibous power projection and other means of affecting events "ashore", so at this point the GTVA's reduced to two basic objectives: destruction of enemy commerce and space control.
You lose access to those destroyer's fighter complements in other areas since they can't be launched rapidly under combat maneuvers.
So you simply deploy the aerospace group in its entirety before engaging. They can follow along or mostly remain behind; attacking them is a low-reward high-risk strategy unlike attacking the destroyer itself. The solution to this one's really very simple.
You let the enemy know exactly where the destroyer is. When in a secure rear area, where the UEF sensor net has been taken down, the destroyers can move about untracked and even use subspace gates. They can't be easily located.
Subspace tracking from point of origin argues that unless you can completely keep UEF ships at least several light-seconds away from the entry point to the system (an unlikely proposition) then it will be entirely possible to track them through multiple jumps and keep tabs on them. Unless all subspace gates jump characteristics are identical, which is doubtful, and the UEF doesn't have any way of basic timestamping their use, which is absurd. If you intend to claim multiple simulatanous activations, then I counter that the total number of such gates in Sol and under GTVA control cannot be high enough to completely swamp the UEF's recon assets.
As a consequence of the above point, with each destroyer you deploy, you free up a vast number of enemy assets once charged with countering its potential deployment. Worse yet, you let the UEF know exactly where to deploy its artillery and horrifying uberbomber squadrons.
This is true of any form of warfare, but it does not happen that way. If you want to accuse people of armchair strategy, at least develop some basic strategic grounding yourself. First, this is a basic manuver warfare concept: overwhelm the local enemy and move on before the rest can effectively coordinate a counterstrike. Even in the subspace age there is a decision cycle. We've seen it at work in FS1 and FS2. If you end the battle in a single salvo and recharge your drives, you can be gone before significant forces are both deployed and able to bring their firepower to bear effectively.
Also, as noted, you still have your own defensive units. If the UEF wishes to go all-in, you can too, or maul their rear areas. Just because you have commited several destroyers to battle does not mean you have commited all destroyers to battle. The enemy defense is still tied up; particularly if you can effectively manage the manuver warfare bit as discussed above.
You will also let the UEF know exactly where to deploy its assets with any offensive action. This is an argument for making your offensives stronger, so that you get more of them back, and more of them succeed. If the UEF's bomber squadrons and artillery are so terrifying, then deployment of a smaller force is simply begging for it to be defeated in detail.
You do not reduce your casualty rate since casualty rate is a function of enemy assets committed as well as exposure time and you'll be allowing that to increase uncontrollably (or even to maximum.)
See above.
You gain little, you risk much. Behavior does not increase strategic fitness.
Not sufficently demonstrated.
With only 3-5 destroyers in Sol, there is good reason the GTVA elects to rarely deploy more than one at a time.
And as I noted it would be entirely possible to briefly augment this strength to much greater levels via short-term (relatively) deployments. This would at least introduce an interesting dynamic into the story as well, as offensive action by either side would be cyclical.
As for the 'will to fight' vs. 'military victory' war, the GTVA cannot win the battle on the field. It must force a diplomatic solution. It does not have the manpower or ability to occupy the UEF's planets and a military victory risks destruction of the all-important infrastructure. What it can do is threaten massive destruction and force concessions.
Which ignores the tenant of the argument willfully; if you win on the field, you destroy their will to fight by default. If you specifically attack their will to fight,
particularly in this situation, you have a very slim chance of being effective militarily or politically.
Now I think the really interesting question from NGTM-1R's argument is, why does the GTVA face any kind of logistical chokepoint at the node? Surely destroyers can just duck back to Delta Serpentis (or further) to refuel. It'd only take a few hours and would allow the GTVA to run a daisy-chain string of loads of destroyers in Sol.
Actually, I'm arguing the exact opposite more or less.
Instead of basing the logistics in Delta Serpentis I'm saying that this is a
destroyer battlegroup, it has to be capable of independent operations over a significant period of time or it's not an effective instrument of war. Arbitrarily, we'll call it a month, though this is probably low. This basically means you can deploy from anywhere within the GTVA, spend a week on surge-tempo operations in Sol, leave, and go back to wherever you came from never to return, on the same set of basic supplies.
The answer has more to do with the GTVA's general force deployments across its territory - given its force commitment to anti-Shivan watch it can't afford to do that. There's also some more particular dynamics of the node, navigation, fuel and logistics that we'll probably get into in a techroom entry.
Which is a commitment that they have come to Sol to fulfil, to gain the population and industrial base to fight the Shivans more effectively. Also given earlier prose about people's failure to believe that the GTVA can protect them from the Shivans, this watch is useless in and of itself; what the GTVA needs to do is prove its fighting arm is still an effective instrument. You can't have your tail wagging your dog.
Unless that's the point for story purposes since it lets the UEF pretend it's a legitimate entry into this contest. Which is bad writing, but there you go.