Pour one can of tomatoes into food processor. Pulse until no large chunks remain, but not yet smooth, 6-8 one-second pulses. Pour into large bowl. Repeat with second can. Set aside.
In large Dutch oven, heat 2 tbsp olive oil over medium-high. When shimmering, add onion, turn down to medium, and cook until onions soften, 5-7 minutes.
Add garlic, anchovy and red pepper flakes. Stir until fragrant, about 30 seconds. Add tomatoes. Bring to a simmer and cook until tomatoes lose their raw flavor, about 10 minutes.
Add water and clam juice. Bring back to a simmer. Add spaghetti, gently pressing it down until it bends and submerges (do not break). Cook, covered, until almost done, about 12 minutes.
Add mussels and shrimp. Stir in gently and cook, covered, until mussels open and shrimp turn pink, about 2 minutes. Add remaining oil and parsley. Season with salt and pepper. Simmer until pasta is fully tender, about 1-2 minutes more.