I've read elswhere on this site that paprika should not be subjected to the high heat used to brown meats. I think flouring the meat before browning facilitates the browning process and absorbs some of the meat juices that would otherwise be stuck on the bottom of the cooking vessel and subjected to undue heat until the pot is deglazed.
Perhaps the paprika is better introduced about 1/2 way through the cooking process.
I agree with the browning process, but I cook my spices before any liquid is added to the pot.
My mom taught me how brown stew meat in flour seasoned with garlic powder and black pepper, thus adding flavor to the meat and the dish. It is my understanding also that when you brown or braise meat it helps seal in the juices and the flavor. I have also not browned the stew meat and my stew did not turn out as good as with browning. I have never had dredging in flour to cause the meat to become slimy. So, my vote is for dredging in flour and seasonings and browning the meat.
To make Beef Stew with leftover pot roast. Add meat, veggies and broth in a soup pot, season with salt and pepper to taste, add a bay leaf any veggies as needed and simmer for about an hour. Thicken with a slury of corn starch and water.