I've had similar thoughts in the past. Databases are very machine-friendly, but too static and inflexible to match the usability of spreadsheets. Spreadsheets are extremely user-friendly, but too inconsistent and unconstrained to be efficient for programmatic access.

It seems like there should be a way to combine the two. Maybe a minimal set of optional constraints (like a separation between data and code) like you proposed would be a good starting point. Make tables a first-class citizen backed by an embedded SQLite database (or something similar); let users write real SQL to query tables in formulas, maybe update the file format a bit to make it easier for programs to parse and access concurrently. Could be an interesting project...