Putting gaps in is also a useful trick to have up your sleeve if you're 3d printing internal threads. If you print threads as continuous bodies, the filament on each layer is effectively a ring which is (because of thread geometry) less supported for part of its length. When it contracts slightly as it cools, it can pull the overhang section of the thread away from the body of the object, and you end up with loose filament strung across the gap.
If you cut gaps along the thread, when it prints you're effectively building a lot of small separated ledges out from a side wall. You don't have that cooling/tensioning effect and there's nothing to pull the filament away from where it's laid down so you end up with a cleaner thread.
That's as long as your retraction settings are well tuned, mind - continuous thread is one long extrusion with no retractions, whereas thread with gaps is potentially lots of islands, depending on how your slicer reacts to the geometry.
I assume this happens on very small threads and/or with thick layers?
I print both depending on size, and a full thread is usually more self-supported, not _less_, while printing faster to booth. Toothed threads tend to suffer from curling more easily when comparing at the same overhang slope, and are weaker structurally.
I'm using toothed threads for larger threads to save on time/material usually, or oddball constraints.
I can see why you would get the effect you're describing, but this would only happen if you're printing with insufficient Z resolution in order to support the overhang of the thread. I cannot see how a toothed thread would improve in such a scenario.
I'm a bit surprised by this. 2mm pitches are well printable at .2, although I usually don't use the stand ANSI/DIN profiles, but limit the overhang profiles manually depending on the material (from 45 up to 70, really) to improve them. Still, at 2mm, this shouldn't be necessary.
Maybe the slicer you're using is doing something odd.
Keep in mind that if the filament string looks pulled in a full thread, a toothed thread with the same settings will be even weaker. In such cases it will change the result to localized sagging areas, where the structural element is just the start/end of each tooth.
A screw, even plastic one, will easily self-thread into the thin amount of plastic remaining, but that doesn't mean that the thread works as intended structurally.
If you have issues with smaller threads my reccomendation is to print an undersized cylinder and use a tap for best results, or just slightly undersize the hole and self-thread instead.
If you cut gaps along the thread, when it prints you're effectively building a lot of small separated ledges out from a side wall. You don't have that cooling/tensioning effect and there's nothing to pull the filament away from where it's laid down so you end up with a cleaner thread.
That's as long as your retraction settings are well tuned, mind - continuous thread is one long extrusion with no retractions, whereas thread with gaps is potentially lots of islands, depending on how your slicer reacts to the geometry.