Paris and Europe in general organize their rail services to be more conducive to a unified fare structure. The European hierarchy of metro - S-Bahn - regional - intercity is distinct from the American hierarchy of subway - express subway - commuter rail - intercity. The RER is a S-Bahn style system which means it blends our notions of an express subway with commuter rail. It's a very different approach that comes with disadvantages and advantages.
A RER style train implemented in NY would look very different from our commuter railroads. To give an example, imagine LIRR trains from its shorter branches being diverted to run via Queens Blvd express tracks, then making only express stops in Manhattan, finally ending on one of the shorter NJT branches. A lot would have to be changed to make that work. Fare collection by conductors would not be feasible and would have to be replaced with zoned fare gates. The rolling stock of LIRR/NJT would be unsuitable with their narrow aisles, seating designed for low turnover (by that I mean the seat is intended to be occupied by one person per trip) and 2 doors per 85'. See Fig.1, RER trains are closer to subway stock.
It's intended that LIRR passengers all have a seat ((necessary since they operate routes up to 60 miles in length), as such the rolling stock does not cope well with standees. Their dwell times would suffer immensely if you applied subway loads to them. That's why "CityFare" was restricted to weekends only - low demand.
Their crews are one conductor, one locomotive engineer and the rest being assistant conductors for the sake of covering fare collection. NYCT had fare collection via conductor with Train to the Plane and it too had a corresponding fare premium.
Many transit bloggers who unfavorably compare American commuter rail to European S-Bahns are deeply critical of the inefficiency of having crew checking tickets, but ignore the unsuitability of S-Bahns for longer commutes.
Fig.1