But it's different than object notation in JS, and considering JSON stands for JavaScript Object Notation, I think dot notation would have been more appropriate

But it's different than object notation in JS, and considering JSON stands for JavaScript Object Notation, I think dot notation would have been more appropriate for JSON Pointer (and by extension JSON Path). As a bit of a rebel myself, I use dot notation when describing a location in a JSON document, unless I'm forced to use the slash for something like JSON Pointer.