Surely some internals of the engine will be running "dry" for a short time after a filter change i.e. until the filter becomes full and passes oil. However the makers do not suggest priming the new filter. Priming a filter is a messy job that I have always done, but my question is, am I wasting my time?
I've never seen an owner's manual or service manual for a passenger car/truck/van that advises priming an oil filter either, as you said in your question too. So if the manufacturers don't say to do it, then you don't need to do it.
If your oil filter is in such a place that you can add some oil & get it attached without easily spilling oil all over the engine, floor, or yourself, then it couldn't hurt.
But many engines I've seen have the oil fill cap on top of the valve cover. Especially if there's only one valve cover (inline 4 or 6-cyl), when you pour in new oil it will be flowing down through the engine anyway.
So when you start it a minute later (as recommended in service manuals I've seen before "topping it off") there will be some oil coating some of the engine, probably a lot more than if it had been sitting overnight. Along with fresh oil and a still-warm engine, I don't think there will be enough extra wear to worry about.
I wouldn't risk spilling oil everywhere, so I don't do it. And mechanics I've seen & talked to don't do it either. I wouldn't say you're wasting your time, but I think you could be spending it more productively doing something else.
If you can prime it, you should. I mean, if the filter sticks out sideways, there is just about no way to prime it and not make a mess. I have a car where I have an element filter which goes in the top of the engine. There is no way to prime it (as the oil would just run back down into the engine anyway). The reason you prime it is to try and minimize the amount of time the engine is ran without oil. The shorter the better (obviously). Always make sure you put new oil on any seals which are on the filter as well. This will help for a proper seal.
Engines will last longer if primed, that's a fact Some Engines don't need to be primed just fill the filter with oil when you change. Other's have a mechanism to stop oil draining back to the sump such as Peugeot and some Renault's. Always use the manufactures oil filter with these cars to ensure the drain back valve is working correctly. Prime oil filter as best you can always.