Yes this is a common scenario for dual homed businesses. Although, you don't want to have each Internet facing gateway dual homed, i.e. your diagrammed topology is over-engineered and will result in unnecessary downtime. Also, you ideally want your ISP links separated across physical distance, i.e. at different locations, for physical redundancy as ISP's typically share the same cable plant into your building/location. Default gateway refers to your internal gateways, i.e. how your inside IP hosts reach the Internet. That's why your diagram says "provider", to delineate between inside gateways and outside gateways.
As for ingress traffic from Internet Service Providers, or providers, that is where BGP comes into play. Noction.com's The Inbound Traffic Engineering article states:
To influence the inbound traffic path, customers can use certainattributes (such as MED, AS-PATH, BGP communities) in the updates sentto their providers. Another method is based on the longestprefix-matching behavior and can be accomplished by the BGPconditional route injection.