The Tejas does via CNB, I think. It already has equivalent, if not higher fares, than the Swarna Shatabdi, so I doubt people will protest against "upgradation". The overnight trains like Lucknow Mail and Lucknow AC go via BE-MB. Amongst day trains, only Lucknow Jn-ANVT Double Decker does via MB.
A VB won't run via MB. That route is slower, despite being twenty kms shorter. It will take the exact route as the Shatabdi/Tejas takes, via Kanpur Central.