Chain hit blessings are powerful on paper but in practice they suffer from too many limitations. If you miss the target, or block, or push, the combo resets to zero and you have to start again.
While the former two make sense, I don’t think pushing should break an attack combo if you immediately chain into the push-attack right afterwards. On some weapons the push attack is better for certain things like single target damage or horde clear and it is common to incorporate them into combos.