Is there a theoretical reason for why we should have better chances at correctly imputing missing values for some (user_id, movie_id) combinations with matrix factorization and similar techniques vs. just building a regression model with ratings as target and (user_id, movie_id, other_features) as right hand side variables?

The regression-based approach would unlock the opportunity of using as regressors explicitly (user’s age, income, etc., movie genre, budget, etc.) and implicitly (user and movie embeddings). I guess that would be awkward to do in the context of matrix factorization.