In reality, that's why the skirt is used. It's meant to ensure you have a good steady flow before starting the print proper. If it's not causing problems on your actual prints, I wouldn't worry about it unless you're also having other inconsistent extrusion. It is possible you have a partial clog or some other problem.
If you want to delve into it, all of those things you describe are under control of the gcode generated by your slicer. Mine does not do the skips on the skirt. When I've got my 1st layer set properly, it prints a solid purge line (I have mine tweaked to start with a thick blob to catch dangling filament, then a narrow strip, a thicker strip and finally a 5mm run of 0 extrusion) them moves to print one continuous skirt line that adheres perfectly to the bed. Well, most of the time.
You can compare the gcode produced by various slicers to see if there are any observable difference. Gcode files are plain text so you can open them up in a text editor to see what's going on.