Most businesses outgrowing Access don't need a smaller, cheaper database, they need a real web application built around the same data and logic that Access was approximating with tables, forms, and macros. The data itself is almost always worth saving, years of records, relationships between tables, business rules buried in a macro somewhere, and a real migration preserves all of that instead of starting from a blank slate.
The harder part isn't moving the data, it's understanding what the Access database's forms and macros were actually doing operationally, since that logic represents years of someone's accumulated business rules, often undocumented anywhere except inside the database itself. We reverse-engineer that logic as part of the migration so the new system does what the old one did, correctly, not just what a generic replacement template assumes it should do.