In the oven, that heat is coming from all directions more or less equally. On the stovetop, the heat is coming only from the bottom. This can potentially cause convection, and almost certainly requires occasional stirring (especially for larger batches), meaning that the ingredients are being moved around. The combination of the ingredients being heated more when they're at the bottom and the movement can cause them to start breaking apart, and generally cook unevenly.
Personally, I only find this to be an issue with beans and meat (and it's not something that's going to cause failure; it's really just a refinement) but if you are making an especially large batch of stew, you may want to try the oven.
Browning ingredients (both meat and vegetables including the aromatics) before doing a braise or stew (which is what slow cookers do) helps develop depth of flavor, through the Maillard reaction where proteins and carbohydrates react together to create a myriad of flavorful compounds. Vegetables that are high in sugar, such as onions or leeks, and even carrots may also have some caramelization, where sugars react with each other, again creating flavorful compounds.
Especially with beef, these deep browned flavors are often what people associate with the product, and what they expect to taste.
On the other hand, browning almost by definition overcooks the outside of meat well past well done, so it is somewhat drier and tougher, although this can be mitigated by a long braise Some experts recommend browning only on one side of cubed meat, to compromise between getting flavor development, and getting good texture.
The one thing browning or searing doesn't do is "seal in the juices"; that is a myth that is well de-bunked.
The choice to brown or not brown is one of taste and balance. It is traditional in many recipes, especially of Western European heritage. There are many traditions where browning is not as frequent, including true Mexican cuisine and many Asian cuisines.
Choose what seems most appropriate and tasty to you in a given dish. Personally, I like the flavor development, and almost always opt for browning.
Best Answer
It has nothing to do with meat absorbing liquids, that doesn't happen just as you explained it. Once meat has become dry, it doesn't get succulent again by somehow spongeing up liquid. The recipe is right to have you wait before serving though, because the flavors keep improving at least for the first day after cooking a stew. It is about aroma, not about texture.
For more detail, see What causes flavors to "marry"? and What happens chemically when flavours 'mingle'?, probably also other questions.