Ah, yeah, range of 0.138 and deviation of 0.039 seem like they’d cause you a number of issues. For reference, here’s my latest run (130c nozzle and 60c bed, probing in the center after having run a Z_TILT_ADJUST
just to make sure a skewed gantry doesn’t lead to inconsistent Z axis movement):
PROBE_ACCURACY at X:110.000 Y:110.000 Z:10.000 (samples=10 retract=2.000 speed=3.0 lift_speed=3.0)
probe at 110.000,110.000 is z=-0.185000
probe at 110.000,110.000 is z=-0.201250
probe at 110.000,110.000 is z=-0.193750
probe at 110.000,110.000 is z=-0.188750
probe at 110.000,110.000 is z=-0.187500
probe at 110.000,110.000 is z=-0.185000
probe at 110.000,110.000 is z=-0.207500
probe at 110.000,110.000 is z=-0.202500
probe at 110.000,110.000 is z=-0.202500
probe at 110.000,110.000 is z=-0.197500
probe accuracy results: maximum -0.185000, minimum -0.207500, range 0.022500, average -0.195125, median -0.195625, standard deviation 0.007815
So that time I got a range of 0.023 and deviation of 0.008. That’s still not as good as I’d like, but good enough to be usable.
I’m not sure why your probe seems to be significantly less accurate. It would be good to gather data from more folks to get an idea how widespread the problem is.
Just checking, but have you ruled out any mechanical issues like loose bed screws (accessible via the cutouts of the magnet on the heated bed) or wobbly extruder mount? Anything that leads to the bed or extruder deflecting when the nozzle taps the bed will probably throw the process out of whack.
As for using a separate probe… I really like the idea of a nozzle probe, to be honest. Not needing to mess with the Z offset when changing nozzles, etc. is nice. So I’m hopeful that Sovol + the community can find a way to improve the accuracy of the existing hardware. 
Edit: Interestingly, probing slower (1 mm/s instead of the default 3 mm/s) gives me a much more consistent result, but it also results in a lower probed distance:
probe accuracy results: maximum -0.165000, minimum -0.175000, range 0.010000, average -0.168875, median -0.168125, standard deviation 0.003555
Presumably the force at which the probe hits the bed affects the trigger point, with a higher speed pressing into the bed more before triggering. So there might be something to this—I can live with slower bed meshes if they are more accurate—but it would take more investigation to adjust the Z offset for a slower config.