In many cooking resources, "low and slow" is given as a solution to cooking juicy, tender meat (after it has been seared). Cooking slowly is also highly recommended when making stews and various other sauces.
My question is - what are the downsides? Is going too "low and slow" will make your meat soggy? Can you ever be "too slow"?
Low and slow is best for certain types of dishes and certain cuts of meat. Meats that have a higher percentage of connective tissues in them come out tough if you don't break that collagen down. Extracting that also adds depth and richness to the dish.
Cuts that are just the muscle and marbled fat, on the other hand, don't really benefit from that. That's why the stews and soups you mentioned, where you are shooting for a rich melange of flavors, call for those cheaper cuts.
A burger, steak, stir-fry would all come out bland and relatively flavorless using that method.
Now, sometimes there is a variation on this to more evenly cook the meat - Cook's Illustrated has a method where you cook a thick steak in the oven at a low temperature so it's evenly cooked to medium-rare throughout, but then you finish the steak by searing in a hot skillet or pan. The idea there is they want the sear, but they want the maximum amount of meat throughout to be medium rare and not be well-done/grey.
The big downside, of course, is time. You don't always want to spend all day cooking something.
For relatively thin pieces of meat (a steak, a chicken breast, a fish fillet) there's just no need to take a long time making it. Worse, you risk making it so tender that it just falls apart. Pulled pork is a wonderful thing, but some days you want slices.
Other cooking methods can add more flavor. In addition to the Maillard reaction, flavorful fats in sautee can bring flavors of their own. Cooking on a grill introduces smoky flavors.
Low and slow maximizes tenderness, but there are other desirable textures. Frying brings crunchiness, which you can't get from low-and-slow. Baked fish takes on a firm texture. And so on.
Low and slow is a crucial tool to have in your arsenal, but it's not the only technique you should learn. Some days you just want to slap something in a pan.
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.
