Problem of different spaces between subscripts and letters in math mode

After some testing I found that loading \usepackage{bm} significantly improves the spacing. As David points out in the comment, the kerning is possible, but grouping plays a role here. Obviously his package bm does better job on \boldsymbol than amsmath. Just remember to load bm after amsmath and after your font packages!

It is a feature of the font and TeX's font parameters.

While TeX does have some fontdimen parameters which control subscript positioning the main controller here is the font metrics where Tex is using the kerning information to pull (or not) subscripts under italic sloped base. However the visual gap also depends on which pixels are black compared to the specified rectangular bounding box of the glyph, and TeX has no knowledge of that at all.