I've never been able to figure out why manufacturers put EZ lube fittings on anything other than boat trailers. You do not consume grease in the bearings. Anytime you inject grease into the cavity, you need to know how much volume is available vs. how much you are injecting. If you put excessive grease in the bearing cavity, it will have to escape. The easiest escape path is through the axle seals.
Once grease leaks past the axle seals, it can enter the brake chamber (drum brakes). This will cause braking problems. Here's a picture of a brake drum with a leaking seal and contamination from the grease. In this case, the seal was defective and grease had not been injected into the EZ Lube, but it still conveys the point:

My Opinion: Adding new grease through an EZ Lube fitting does not remove worn and contaminated grease from the bearings, and can possibly result in leaks and contaminated brakes. Periodically, the bearings should be cleaned and packed with fresh grease. While doing so, always install new grease seals. And while your at it, it's a good time to check your brakes too.