  Breaking parity (P) symmetry in C$_6$ symmetric crystals is a common routine
to implement a valley-topological phase. At an interface between two crystals
of opposite valley phases, the so-called valley topological edge states emerge,
and they have been proven useful for wave transport with robustness against
120$^\circ$ bending and a certain level of disorder. However, whether these
attractive transport features are bound with the valley topology or due to
topological-irrelevant mechanisms remains unclear. In this letter, we discuss
this question by examining transport properties of photonic edge states with
varied degrees of the P-breaking that tune the valley topology, and reveal that
the edge states preserve their transport robustness insensitive to the topology
even when the P-symmetry is recovered. Instead, a unique modal character of the
edge states -- with localized momentum hotspots around high-symmetric $K$
($K'$) points -- is recognized to play the key role, which only concerns the
existence of the valleys in the bulk band structures, and has no special
requirement on the topology. The "non-topological" notion of valley edge states
is introduced to conceptualize this modal character, leading to a coherent
understanding of bending immunity in a range of edge modes implemented in C$_3$
symmetric crystals -- such as valley topological edge states, topological edge
states of 2D Zak phase, topological-trivial edge states and so on, and to new
designs in general rhombic lattices -- with exemplified bending angle as large
as 150$^\circ$.
