The downside is flavor.
Although you can get some great flavors by extracting collagen and such out of meat, you don't get any browning from the Maillard reaction.
The browning is the result of new chemical compounds being produced ... but it doesn't happen until you get to around 285°F / 140°C.
It's part of the reason why steamed chicken has nowhere near the flavor of grilled. (poached is similar to steamed, but you're also moving some of the existing flavors into the cooking liquid. And you can compensate by using a flavorful liquid to get flavors into the poultry).
.... but in your scenario, you specifically mentioned 'low and slow' only after searing, so we still do have the Maillard reaction. Maybe it's not as deep as it would have been if we had kept the food over higher heat the whole time, but it's typically a good trade-off. (resulting in food that tastes good, and doesn't require 5 minutes to chew each bite).
As for the 'soggy' bit -- unless you're cooking it in a liquid, you won't have more liquid in the meat than when you started cooking it. Even if you started with a brined or injected bird, it's actually quite difficult to end up with 'soggy' meat. 'Mushy' maybe ... if you overcooked via a slow poach.
Sou vide is effectively poaching, as the juices that get squeezed out have nowhere to go, so stay in the bag right next to the meat. Sou vide on its own (without a sear before or after) is actually quite bland. You really need to add herbs and such to compensate.