I just replaced my mechanical pump with an electric pump and it's a night and day difference!
The electric pump is more efficient and my engine runs a lot smoother as well.
Ya there really isn't a reason that an electric pump should make an engine run "smoother" compared to a mech pump unless there was an issue with the mech set up, like air intrusion or starvation for example.
I do run electric for the reason of easier priming, and because good quality replacement mech pumps are getting harder to come by. ….as are electric however. But there are more options for electric as there are for mech pumps. And if installed in a smart way, electric pumps can be easier to change out upon failure, compared to a mech pump. Otherwise I would still be running mech pumps.
The ease of priming with an electric pump, after running out of fuel or whatever; can really be a big deal if you run your batteries down in the middle of nowhere trying to re-prime a fuel system on a mech pump engine. And having a more positive and quicker prime to the injection pump, reduces wear on the injection pump and the starter.
But don't quickly scab together an cheap e pump setup in a hokey way and expect it to last and give good results. Install a good pump, in an appropriate manner.