If you want to retain the higher harmonics, you don’t want the LPF.
An external LPF can do a better job than the one in the bass depending on the filter design but it is also additive with the bass tone circuit so they can compliment one another.
Just out of curiosity - when using a pedal like Broughton's HPF+LPF, if you set the LPF at the 20k setting, wouldn't that pretty much be like it wasn't there at all, regarding high frequencies?