Both Central and XC at some point tried diverting some of their Cardiff services via Worcester, but evidently again it worked out as too much pain (journey times increased by about 20-30 minutes) for not enough gain.
I was looking at this just the other day and was surprised to find (on Realtime Trains) the following XC services which run between Birmingham and Cheltenham via Stourbridge and Worcester but don't stop:
1V01 0500 Birmingham New Street - Cardiff Central
1V02 0537 Birmingham New Street - Cardiff Central
1M87 2105 Cardiff Central - Birmingham New Street
1M80 2014 Paignton - Birmingham New Street
I guess it's to maintain route knowledge but it seems a pity not to stop at Shrub Hill. I've always thought Worcester deserves a better service on the Cross country route.
Off topic but many years ago (70s) I vaguely remember travelling from Birmingham to Worcester via the Lickey on a Paddington - Paddington train. I guess this would have run via High Wycombe, Solihull to Birmingham New Street then back to Paddington via Worcester and Oxford.