SaaS is not a new idea and has been renamed multiple times.

In the 70s, it was called "time-sharing". Instead of buying a mainframe, you got a CICS application instance on a mainframe and used that. (tangentially, spare time on these built-out nation-wide dialup-supported networks is what gave birth to CompuServe and GEnie).

In the dot-com era, it was called "application service providers". Salesforce and actually started in this era (1999). So did NetSuite. This was the first attempt to be browser-based but bandwidth and browsers sucked then.

I think PaaS is a more recent software paradigm, albeit a far less successful one.