Other geocoding systems will return in the result a uniquie identifier (UID) - so that if that address is queried again in future it can be linked to the existing location rather than a new entry created.
I don't know much about other geocode systems as you mentioned, but you need to understand better how a geocoder works in ESRI to know how to implement such a solution, assuming that's what you're after.
Short long story, a geocoder is a quicker way (using an indexed table) to find information for coordinates. When creating the geocoder, you also define its output structure, based on the available data that geocoder is attached to (which is an indexed table).
Normally, a geocoder will return the data based on the coordinates. You can build your own geocoder and decide that it returns some kind of ID, but if there's an internal cache mechanism to monitor your calls and retrieve previous values? definitely not out of the box, but you can probably create one of your own. Also, when using ESRI's world geocoder / public geocoders, there are some legal requirements for billing purposes when using the geocoder over a certain amount of calls per month, so I don't see how that can work with the mechanism you mentioned when calling a public geocoder.
There are online resources you can read about it - What is geocoding?—ArcMap | Documentation