What are some usage-based SaaS pricing models that are not based upon user licensing fees but are simple to understand/explain?

Dropbox.com, pay for the data.
Zapier.com, pay for the triggers.
CRMs (most of), pay for the contacts.

Etc.

Some also mix in "agent" or "per user" fees because in today's world, a small company can do a lot of business and a "large" company (many employees) may do less.

A mixed pricing model, that is still simple enough, helps the provider capture more value and effectively practice price discrimination without getting accused of it.

"You can afford more? Well you should pay more!"