Sprint drives still need to recharge. Just look at the Carthage. Your plan of having it jump from one engagement to another would end up with it getting caught in the middle of a recharge cycle and then easily disposed of by a hunter-killer team. Especially since neither the UEF captain or chief engineer are terribly likely to understand the limits of the ship. And don't think you can use the original crew. Just because they defected doesn't mean they're willing to take up arms against their former comrades, and it doesn't mean you should let them.
Planning to use the Labouchere the same way Steele uses Serkr just isn't going to yield huge dividends for the simple reason that it's got less than a third of Serkr's firepower and none of their experience.
As for the Duke, one Hyperion changes absolutely nothing. As an escort cruiser, it's not that much better than the Sanctus. The Hyperion is a fast attack cruiser, meant for hit and run strikes. The issue is that just one isn't much better at that job than a gunship wing, which is why the GTVA pretty much always deploys them in pairs.
I really can't think of any engagements in WiH where the outcome would have been seriously altered by adding a Chimera or a Hyperion to the UEF side.
These two might be useful (in that they're better than nothing) but far more useful to the UEF would be tearing them apart to learn everything they can. Which is probably what happened. The Duke and Labouchere are probably mostly-empty hulks by now.
The Agincourt and Solace are a different matter because they offer actual strategic benefits to the UEF, unlike the other two ships.
I call shennanigans on that one. In "conversations from WiH" it's made very clear that the UEF has <10 people with the same flight hours as Lorna Simms, since they're letting their aces stay on the front and eventually die. They could really use a few more aces, especially those familiar with GTVA ships. Disable the IFF and someone might hesitate for a second, in the slight case that it's a friendly ship that got it's comms and sensors destroyed.
Wouldn't really work long-term, but even slight hesitation can win a close dogfight.
Also, GTVA pilots are probably the masters of beam-disarming, if AoA is anything to go by. They'd never make it through AoA alive if not for those beam killing skills, and while the UEF had to adapt to that in 18 months, the GTVA has been in the beam killing business for 18 years.
You know what would be more useful than having him fly? Having him teach new pilots, which is what the GTVA does with their aces. The UEF doesn't need more aces, they need fewer rookies dying because of rookie mistakes. I also doubt Bei would even be willing to fight the GTVA.
There's also the cardinal rule about defectors: you don't trust them. This is a real life one. If they betrayed their country, what says they won't have second thoughts and betray you as well? Why do you think Admiral Bei is basically just a consultant now?