The relational query model (it's operators and set algebra) is a poor fit for common business inquiries. I view SQL as a practical syntax for encoding relational queries; SQL has deviated from the pure model when the model failed to address a real world business problems. I see SQL as a success, in that it works and applies the relational model to real world concerns.

What is intuitive to users is the idea of related files/tables, and this really doesn't have much to do with the relational algebra. While we have implemented HTSQL using SQL, this is an implementation choice -- our experiment is syntax/semantics, we didn't want to be in the business of data storage and query optimization, and, we use (the incredibly awesome) PostgreSQL. HTSQL's logical query model depends upon is a tabular based abstract storage.

Oh, the relational query model based on relational algebra! I thought you wrote "relational model".

For what it's worth, a join is indeed part of relational algebra - it's a composition of binary relations.