How does this compare to a pure, recursion-free subset of Prolog? Not counting cosmetic differences, e.g., in Prolog, relation arguments are positional, whereas in the relational model, attributes have names.
If you're interested in connections between relational algebra (and SQL, and databases) and logic programming, you should look at Datalog, which is a restricted subset of Prolog that is akin to relational algebra plus fixed points (transitive closure, for example). In particular, Datalog forbids compound terms (like lists) and recursion in a negated position.
I think Datalog without recursion/fixed-points is precisely as powerful as relational algebra, but I don't have a proof handy.
But, even in the absence of compound data types, the answer to a Prolog query may contain free variable, whereas the answer to SQL query may not. So you do have a point.
(You don't need to be recursion free. Just restrict your recursion very carefully.)
Eg for data interchange compare json vs evaluating any random javascript expression. The latter is strictly more powerful than the former. The former is better.
Or an example in the other direction: imagine Haskell-Prime, like Haskell, but you can mutate every variable. Strictly more powerful, but awful. (Or imagine adding GOTO to your favourite programming language.)
Wrong. The power of Haskell mostly comes from how easy it is to reason about code. Your proposed Haskell-Prime would be less powerful in this sense.