Looks like depth is calculated incorrectly for subscripts applied to subscripted expressions. I guess the assumption in the pretty printer code is that the depth needs to be increased for every subscript, but that's not necessarily true, since the second and additional subscripts are placed beside, not beneath, the previous subscripts.
(%i2) box (foo);
╔═══╗
(%o2) ║foo║
╚═══╝
(%i3) box (foo[a]);
╔════╗
(%o3) ║foo ║
║ a║
╚════╝
(%i4) box (foo[a][b]);
╔═══════╗
(%o4) ║(foo ) ║
║ a b║
║ ║
╚═══════╝
(%i5) box (foo[a][b][c]);
╔══════════╗
(%o5) ║((foo ) ) ║
║ a b c║
║ ║
║ ║
╚══════════╝